finite p groups all of whose d generated subgroups are powerful let p be an odd prime we study d powerful p groups i e finite p groups all of whose d generated subgroups are powerful for p 5 we show that any powerful p group g is d g powerful where d g denotes the minimal number of generators of g moreover for a finite p group g we prove that if there is a positive integer 2 m d g such that g is m powerful then all subgroups of g are powerful i e g is modular our results lead to a new characterization of dually strongly balanced finite p groups furthermore minimal non powerful finite p groups are determined completely up to isomorphism for finitely generated pro p groups some analogous results are proved for instance if for a torsion free finitely generated pro p group g there is a positive integer 2 m d g such that all m generated subgroups of g are powerful then all subgroups of g are powerful

on the number of conjugacy classes of finite nilpotent groups abstract we establish the first super logarithmic lower bound for the number of conjugacy classes of a finite nilpotent group in particular we obtain that for any constant c there are only finitely many finite p groups of order p m with at most c m conjugacy classes this answers a question of l pyber

groups without faithful transitive permutation representations of small degree abstract a subgroup h of a group g is core free if h contains no non trivial normal subgroup of g or equivalently the transitive permutation representation of g on the cosets of h is faithful we study the obstacles to a group having large core free subgroups we call a subgroup d a dedekind subgroup of g if all subgroups of d are normal in g our main result is the following if a finite group g has no core free subgroups of order greater than k then g has two dedekind subgroups d 1 and d 2 such that every subgroup in g of order greater than f k has non trivial intersection with either d 1 or d 2 where f is a fixed function independent of g examples show that the dedekind subgroups need not have index bounded by a function of k and the result would not be true with one dedekind subgroup instead of two we exhibit various related properties of p groups and infinite locally finite groups without large core free subgroups including the following if g is a locally finite group with no infinite core free subgroup then every infinite subgroup of g contains a non trivial cyclic normal subgroup of g we also exhibit asymptotic bounds for some related problems including the following if a group g has a solvable subgroup of index n then g has a solvable normal subgroup of index at most n c for some absolute constant c if g is a transitive permutation group of degree n with cyclic point stabilizer subgroup then g n 7

hausdorff dimension pro p groups and kac moody algebras every finitely generated profinite group can be given the structure of a metric space and as such it has a well defined hausdorff dimension function in this paper we study hausdorff dimension of closed subgroups of finitely generated pro p groups g we prove that if g is p adic analytic and h c g is a closed subgroup then the hausdorff dimension of h is dimh dimg where the dimensions are of h and g as lie groups letting the spectrum spec g of g denote the set of hausdorff dimensions of closed subgroups of g it follows that the spectrum of p adic analytic groups is finite and consists of rational numbers we then consider some non p adic analytic groups g and study their spectrum in particular we investigate the maximal hausdorff dimension of nonopen subgroups of g and show that it is equal to 1 1 d 1 in the case of g sld fp t where p 2 and to 1 2 if g is the so called nottingham group where p 5 we also determine the spectrum of sl2 fp t p 2 completely showing that it is equal to 0 2 3 1 some of the proofs rely on the description of maximal graded subalgebras of kac moody algebras recently obtained by the authors in joint work with e i zelmanov

uniform groups and lie algebras abstract in this text we study the exp log functors for the categories of uniform groups and uniform lie algebras

an architecture for addition and subtraction of long word length numbers in the logarithmic number system an architecture is described for performing addition and subtraction of numbers in the logarithmic number system using small lookup tables previous implementations require approximately 4 2 sup f words for f bits of precision in the fraction the author shows how to reduce the size of the lookup table to fewer than 18 f 2 sup f 2 words the key to this is the use of a linear approximation of the nonlinear functions stored in the lookup tables the functions involved are highly nonlinear in some regions so variable size regions are used for the approximation the replacement of the f exponential dependence on the number of words by f 2 allows roughly 50 more bits of fractional precision to be obtained for a given amount of rom the architecture is mathematically analyzed yielding explicit expressions for all design parameters the approach is illustrated with an example logarithmic addition and subtraction unit using 32 b words with 30 b exponents containing 22 fractional bits a factor of 118 reduction in table size compared to previous techniques is achieved for this example

comments on an architecture for addition and subtraction of long word length numbers in the logarithmic number system by d m lewis d m lewis ibid vol 39 no 11 p 1325 36 nov 1990 recently described an architecture for performing addition and subtraction in the logarithmic number system using a taylor series approximation and rom tables here it is shown that a 25 improvement can be achieved in the table used to implement addition this improvement is significant when lewis technique is used to implement variations of the logarithmic number system which do not require the subtraction logarithm

error free solution to a toeplitz system of equations a numerical method which allows error free computation of the solution to a toeplitz system of equations is developed the method requires that the system of equations have rational entries to avoid error that is inherent in floating point arithmetic multiple modulus residue arithmetic is applied to a modified version of the levinson algorithm and to an algorithm presented by s y kung and y h hu 1983 the error free method has a highly parallel structure and can be implemented with existing software and hardware the exact method presented here serves as an outline for the general approach to the development of error free solution methods

on the exponent of a finite group with an automorphism group of order twelve abstract suppose that a frobenius group fh with kernel f of order 4 and complement h of order 3 acts coprimely on a finite group g in such a manner that c g f 1 and c g h has exponent e we prove that the exponent of g is e bounded earlier results of this nature were known only for metacyclic frobenius groups

on the relation between upper central quotients and lower central series of a group let h be a group with a normal subgroup n contained in the upper central subgroup zch in this article we study the influence of the quotient group g h n on the lower central subgroup yc lh in particular for any finite group g we give bounds on the order and exponent of yc l h for g equal to a dihedral group or quaternion group or extra special group we list all possible groups that can arise as yc lh our proofs involve i the baer invariants of g ii the schur multiplier m l g of g relative to a normal subgroup l and iii the nonabelian tensor product of groups some results on the nonabelian tensor product may be of independent interest

implementation of four common functions on an lns co processor we propose a scheme for evaluating four commonly used functions namely 1 inverse trigonometric functions 2 trigonometric functions 3 the exponential function and 4 the logarithmic function with the help of a logarithmic number system lns processor a novel idea of series folding has been introduced for computing the above functions expressed in the form of infinite series we also show that with a suitable choice of the radix for the lns we can evaluate exponential and logarithmic functions without using any extra hardware

sound quality characteristics of refrigerator noise in real living environments with relation to psychoacoustical and autocorrelation function parameters psychoacoustical and autocorrelation function acf parameters were employed to describe the temporal fluctuations of refrigerator noise during starting transition into from the stationary phase and termination of operation the temporal fluctuations of refrigerator noise include a click at start up followed by a rapid increase in volume a change of pitch and termination of the operation subjective evaluations of the noise of 24 different refrigerators were conducted in a real living environment the relationship between objective measures and perceived noisiness was examined by multiple regression analysis sound quality indices were developed based on psychoacoustical and acf parameters the psychoacoustical parameters found to be important for evaluating noisiness in the stationary phase were loudness and roughness the relationship between noisiness and acf parameters shows that sound energy and its fluctuations are important for evaluating noisiness also refrigerator sounds that had a fluctuat

on centralizers in locally finite groups abstract the main result of the paper is the following theorem let g be a locally finite group containing a finite p subgroup a such that cg a is finite and a non cyclic subgroup b of order p2 such that cg b has finite exponent for all b b then g is almost locally solvable and has finite exponent

a characterisation of powerfully embedded normal subgroups of ap group abstract letpbe a prime number andgbe ap group 6 have introduced the notion of a powerfully embedded subgroup ofg our main result gives a characterisation of those powerfully embedded subgroups which are contained in the frattini subgroup ofg whenpis odd whenp 2 the subgroups characterised have a weaker property than powerful embedding this result also yields information on the structure of d maximal 2 groups

overflow underflow free floating point number representations with self delimiting variable length exponent field a class of new floating point representations of real numbers based on representations of the integers is described in the class every representation uses a self delimiting representation of the integers as a variable length field of the exponent and neither overflow nor underflow appears in practice the adopted representations of the integers are defined systematically so that representation s of numbers greater than one have both exponent significant and integer fraction interpretations since representation errors are characterized by the length function of an underlying representation of the integers superior systems in precision can be easily selected from the proposed class

area efficient multipliers based on multiple radix representations in this paper we shall introduce several new algorithms for integer multiplication that are based on specific multiple radix representation of one of the multiplicands we provide extensive theoretical analysis and experimental results for multipliers based on the new representations on 0 18 m cmos technology they provide a clear picture about the advantages of the new method in 64 bit hardware implementations compared to array based classical multiplier and radix 8 based multiplier the proposed multipliers have better area and power consumption compared to reference multipliers

lie rings with almost regular automorphisms let l be a lie ring or a lie algebra of arbitrary not necessarily finite dimension let be an automorphism of l and let cl a l a a denote the fixed point subring the automorphism is called regular if cl 0 that is has no non trivial fixed points by kreknin s theorem 20 if a lie ring l admits a regular automorphism of finite order k that is such that 1 and cl 0 then l is soluble of derived length bounded by a function of k actually by 2 2 earlier borel and mostow 3 proved the solubility in the finite dimensional case without a bound for the derived length in the present paper we prove that if a lie ring admits an automorphism of prime power order that is almost regular then l is almost soluble

some windows with very good sidelobe behavior some of the windows presented by harris 1 are not correct in terms of their reported peak sidelobes and optimal behavior we present corrected plots of harris windows and also derive additional windows with very good sidelobes and optimal behavior under several different constraints the temporal weightings are characterized as a sum of weighted cosines over a finite duration the plots enable the reader to select a window to suit his requirements in terms of bias due to nearby sidelobes and bias due to distant sidelobes

beyond floating point un systeme numerique est propose pour l arithmetique d ordinateur basee sur des fonctions exponentielles iterees l avantage principal est d extirper le sous passement et le depassement de capacite mais il y a quelques autres avantages et ceux ci sont decrits et discutes

measurement of regional environmental noise by use of a pc based system an application to the noise near airport g marconi in bologna abstract measurements of aircraft noise were made at the airport g marconi in bologna by using a measurement system for regional environmental noise the system is based on the model of the human auditory brain system which is based on the interplay of autocorrelators and an interaural cross correlator acting on the pressure signals arriving at the ear entrances and takes into account the specialization of left and right human cerebral hemispheres see reference 8 measurements were taken through dual microphones at ear entrances of a dummy head the aircraft noise was characterized with the following physical factors calculated from the autocorrelation function acf and interaural cross correlation function iacf for binaural signals from the acf analysis 1 energy represented at the origin of delay 0 2 effective duration of the envelope of the normalized acf e 3 the delay time of the first peak 1 and 4 its amplitude 1were extracted from the iacf analysis 5 iacc 6 interaural delay time at which the iacc is defined iacc and 7 width of the iacf at the iacc wiaccwere extracted the factor 0 can be represented as the geometrical mean of the energies at both ears a noise source may be identified by these factors as timbre

pro finite p adic lie algebras abstract let p be a prime number a finite nilpotent lie ring of characteristic a power of p is called finite p a pro p lie ring is an inverse limit of finite p lie rings pro p lie rings play a role in lie theory similar to that played by pro p groups in group theory every pro p lie ring admits the structure of a lie algebra over the p adic integers furthermore every p adic lie algebra of finite rank as a p adic module has an open pro p subalgebra we make a detailed study of pro p lie rings in terms of various properties including their topology prufer rank subring growth and p adic module structure in particular we prove the equivalence of the following conditions for a finitely generated pro p lie ring l l has finite prufer rank l is isomorphic to a closed subring of gl v for some p adic module v of finite rank and for sufficiently large n the lie f p subalgebra w n e 12 t e 22 gl 2 f p t t n is not an open section of l by reducing to the pro p lie ring case we also prove that all engelian pro finite lie rings are locally nilpotent this is a lie theoretic analogue of zelmanov s theorem which states that every periodic pro p group is locally finite

lns with co transformation competes with floating point the logarithmic number system has been proposed as an alternative to floating point arithmetic multiplication division and square root operations are accomplished with inexpensive fixed point methods but addition and subtraction are considerably more challenging recent work has demonstrated that these operations too can be done with similar speed and accuracy to their fp equivalents but the necessary circuitry is complex in particular it is dominated by the need for large rom tables for the storage and interpolation of non linear functions we describe a new co transformation procedure that eliminates much of the rom space and allows the easy synthesis of the remainder in logic and we then evaluate several interpolation methods that might benefit from it synthesised 32 bit implementations are compared with floating point units and show substantial reductions in delay with equivalent accuracy and area

duration sensation when listening to bandpass noises abstract the duration sensation of bandpass noise was examined while changing the factors 1 1and e extracted from the autocorrelation function the white noise and bandpass noises with six center frequencies 125 250 500 1000 2000 and 4000 hz with different bandwidths were used as stimuli a paired comparison test comparing the white noise duration with bandpass noise duration was conducted under the conditions of constant sound pressure level spl 80 db a and rise and fall times 1 ms results indicate that the duration of bandpass noise is judged to be longer than that of the white noise the duration sensation of the bandpass stimuli with longer 1is significantly longer than that of the stimuli with shorter 1 p

redundant logarithmic arithmetic a number system that offers advantages in some situations over conventional floating point and sign logarithmic number systems is described redundant logarithmic arithmetic like conventional logarithmic arithmetic relies on table lookups to make the arithmetic unit simpler than an equivalent floating point unit the cost of 32 bit subtraction in a redundant logarithmic number system is lower than previously published logarithmic subtraction methods the total memory requirement for a 29 bit redundant logarithmic unit is 16 k words compared to 22 k words by the best previously published conventional sign logarithm unit assuming similar addition techniques are employed a redundant logarithmic number system can be implemented with online arithmetic which would be impractical for a conventional sign logarithm number system the disadvantages of redundant arithmetic are typical of redundant number systems first the redundancy doubles the storage requirements for data values second the representation can become ill conditioned especially as a result of iterated multiplications third division and square root operations are more difficult to implement in redundant logarithmic arithmetic

on almost fixed point free automorphisms abstract ideas from the theory of p adic analytic groups are employed in the study of finite groups having automorphisms with few fixed points in particular we prove that the derived length of a finite p group admitting an automorphism of order p k with p m fixed points is bounded in terms of p m k this extends a well known result of alperin dealing with the case k 1 some applications to soluble groups are also given

acoustical properties of aircraft noise measured by temporal and spatial factors abstract acoustical properties of aircraft noise were investigated by means of temporal and spatial factors in sound fields based on the model of auditory brain system see reference 10 the model consists of the autocorrelation and crosscorrelation mechanisms for sound signals arriving at two ears and the specialization of human cerebral hemisphere there are four temporal factors extracted from the autocorrelation function acf 1 sound energy 0 2 effective duration of acf e 3 delay time of the first peak 1 and 4 its amplitude 1 from the interaural crosscorrelation function iacf three spatial factors are extracted as 1 magnitude of the interaural crosscorrelation iacc 2 interaural delay time at iacc iacc and 3 width of the maximum peak of the iacf wiacc it is found that the acoustical properties are well represented by the factors extracted from the acf and the iacf

a hybrid number system processor with geometric and complex arithmetic capabilities the architecture design and performance of a hybrid number system processor are described the processor performs multiplication division square root and square in the logarithmic number system lns domain however the input output addition and subtraction are all executed in the 32 b ieee standard floating point number system with the lns multiplier and pipelined architecture the processor is able to perform the geometric and complex arithmetic very effectively the processor is also shown to compare well to an existing 32 b floating point dsp digital signal processor chip for the same level of cmos technology the performance ratios between the hybrid number system and the floating point processor are shown to be 6 4 1 and 8 1 for division and square root respectively for the complex fft fast fourier transform algorithm the ratio is around 2 1

on pro p groups with potent filtrations abstract in this note we prove that if g is pf group of finite exponent then the exponent of the second homology group h 2 g m divides the exponent of g for every profinite trivial z g module m we introduce the notion of the exponential rank of a pro p group and find a bound for the exponential rank of a pf group

on profinite groups in which commutators are covered by finitely many subgroups for a family of group words w we show that if g is a profinite group in which all w values are contained in a union of finitely many subgroups with a prescribed property then the verbal subgroup w g has the same property as well in particular we show this in the case where the subgroups are periodic or of finite rank if g contains finitely many subgroups g1 g2 gs of finite exponent e whose union contains all k values in g it is shown that k g has finite e k s bounded exponent if g contains finitely many subgroups g1 g2 gs of finite rank r whose union contains all k values it is shown that k g has finite k r s bounded rank

almost solubility of lie algebras with almost regular automorphisms the well known theorem of borel mostow kreknin on solubility of lie algebras with regular automorphisms is generalized to the case of almost regular automorphisms it is proved that if a lie algebra l admits an automorphism of finite order n with finite dimensional fixed point subalgebra of dimension dimcl m then l has a soluble ideal of derived length bounded by a function of n whose codimension is bounded by a function of m and n theorem 1 a virtually equivalent formulation is in terms of a n graded lie algebra l whose zero component l0 has finite dimension m the functions of n and of m and n in theorem 1 can be given explicit upper estimates the proof is of combinatorial nature and uses the criterion for solubility of lie rings with an automorphism obtained in e i khukhro siberian math j 42 2001 996 1000 the method of generalized or graded centralizers is developed which was originally created in e i khukhro math ussr sbornik 71 1992 51 63 for almost regular automorphisms of prime order as a corollary we prove a result analogous to theorem 1 on locally nilpotent torsion free groups admitting an automorphism of finite order with the fixed points subgroup of finite rank theorem 3 we also prove an analogous result for lie rings with an automorphism of finite order having finitely many fixed points theorem 2 2003 elsevier inc all rights reserved

schur multipliers and power endomorphisms of groups abstract we obtain new bounds for the exponent of the schur multiplier of a given p group we prove that the exponent of the schur multiplier can be bounded by a function depending only on the exponent of a given group as a consequence we show that the exponent of the schur multiplier of any group of exponent four divides eight and that this bound is best possible the notion of the exponential rank of a p group is introduced we show that powerful p groups have exponential rank either zero or one

finite groups with an automorphism of prime order whose centralizer has small rank abstract let be an automorphism of prime order p of a finite group g and let c g be its fixed point subgroup when is regular that is c g 1 the group g is nilpotent by thompson s theorem the almost regular results of fong and hartley meixner pettet were giving the existence of a nilpotent subgroup of index bounded in terms of p and c g we prove the rank analogues of these results when almost regular in the hypothesis is interpreted as a restriction on the rank r of c g and the conclusion is sought as nilpotency modulo certain bits of bounded rank the classification is used to prove almost solubility in the coprime case the rank of g s g is bounded in terms of r and p for soluble groups the hall higman type theorems are combined with the theory of powerful q groups to obtain almost nilpotency even without the coprimeness condition there are characteristic subgroups r n g such that n r is nilpotent and the ranks of r and g n are bounded in terms of r and p examples show that our results are in a sense best possible

profinite groups and the fixed points of coprime automorphisms abstract the main result of the paper is the following theorem let q be a prime and a an elementary abelian group of order q 3 suppose that a acts coprimely on a profinite group g and assume that c g a is locally nilpotent for each a a then the group g is locally nilpotent

the unitary cover of a finite group and the exponent of the schur multiplier abstract for a finite group we introduce a particular central extension the unitary cover having minimal exponent among those satisfying the projective lifting property we obtain new bounds for the exponent of the schur multiplier relating to subnormal series and we discover new families for which the bound is the exponent of the group finally we show that unitary covers are controlled by the zelmanov solution of the restricted burnside problem for 2 generator groups

on quaternion free 2 groups abstract two theorems are proved the first of them showing that a modular quaternion free finite 2 group has a characteristic abelian subgroup with metacyclic factor the second classifying nonmodular finite quaternion free 2 groups

improved addition for the logarithmic number system the logarithmic number system lns which offers a wide dynamic range with an independently choosable signal to noise ratio is discussed to realize addition voluminous lookup tables are needed a method is proposed to reduce the storage requirements of these tables by means of chebyshev approximation with unequally spaced partition points

fpga designs with optimized logarithmic arithmetic using a general polynomial approximation approach we present an arithmetic library generator for the logarithmic number system lns the generator produces optimized lns arithmetic libraries that improve significantly over previous lns designs on area and latency we also provide area cost estimation and bit accurate simulation tools that facilitate comparison between lns and floating point designs

powerful p groups have non inner automorphisms of order p and some cohomology in this paper we study the longstanding conjecture of whether there exists a non inner automorphism of order p for a finite non abelian p group we prove that if g is a finite non abelian p group such that g z g is powerful then g has a non inner automorphism of order p leaving either g or 1 z g elementwise fixed we also recall a connection between the conjecture and a cohomological problem and we give an alternative proof of the latter result for odd p by showing that the tate cohomology hn g n z n 0 for all n 0 where g is a finite p group p is odd g z g is p central i e elements of order p are central and n g with g n non cyclic

on almost regular automorphisms of finite p groups abstract in this paper we prove that there are functions f p m n and h m such that any finite p group with an automorphism of order p n whose centralizer has p m points has a subgroup of derived length h m and index f p m n this result gives a positive answer to a problem raised by e i khukhro see also problem 14 96 from the kourovka notebook 1999 e i khukhro and v d mazurov eds the kourovka notebook unsolved problems in group theory 14th ed novosibirsk

closure and precision in level index arithmetic first it is proved that two recently introduced systems of computer arithmetic the level index li and symmetric level index sli systems are closed under the four basic arithmetic operations provided that division by zero is excluded and the operations are executed in finite precision in consequence the li and sli systems are free from the defects of overflow and underflow second measures of precision are discussed and compared third the ranges and local precisions of numbers stored in the li and sli systems are compared with corresponding ranges and local precisions of numbers stored in the floating point system

on efficient implementations of 2 d digital filters using logarithmic number systems the implementation of 2 d digital filters using logarithmic number systems lns s is discussed in detail the properties of such systems are derived with reference to an iterative rounding scheme which allows increasing the accuracy of the filter coefficient representation by using more than one power of the base a the optimization of the base is proposed as an efficient tool for the design of accurate 2 d filters different design strategies are considered together with a discussion of the degree of precision required for the circuits which determine the base of the lns the efficiency and versatility of this approach are demonstrated with several design examples in 2 d

finite precision rational arithmetic an arithmetic unit the foundations of an arithmetic unit performing the add subtract multiply and divide operations on rational operands are developed the unit uses the classical euclidean algorithm as one unified algorithm for all the arithmetic operations including rounding binary implementations are discussed based on techniques known from srt division and utilizing ripple free borrow save and carry save addition average time behavior is investigated

a bound for the exponent of the schur multiplier of a finite p group let p be a prime g a finite p group r the rank of g and e the exponent of g in this short note we will prove that the exponent of the schur multiplier of g divides pe r log2 rlog2p 1p 1

a non abelian free pro pgroup is not linear over a local field abstract in this paper we show that a non abelian free pro pgroup cannot be obtained as a closed subgroup ofgln f wherefis a non archimedean local field andnis arbitrary using a theorem of e i zel manov we deduce some group theoretic properties of linear pro pgroups over a local field our main tool is a recent theorem by pink characterizing compact subgroups ofgln f

the loudness of complex noise in relation to the factors extracted from the auto correlation function abstract the loudness of complex signals which include bandpass noises with different center frequencies complex noise is examined while changing the effective duration of the autocorrelation function e based on a model of the human auditory brain system for subjective response to a sound field the center frequencies of each component of the complex noises were 2000 and 3000 hz so that the perceived pitch was centered on 1000 hz the bandwidth of each component was changed by using a 2068 db octave sharp filter to control the e of the source signal the scale values for the loudness of the complex noises were obtained using a paired comparison method the results showed that the loudness increases with the eof the source signal similar to that of the single noise component centered on 1000 hz the loudness of complex noises having equal sound pressure levels is not constant within the critical band 160 hz

powerfully nilpotent groups abstract we introduce a special class of powerful p groups that we call powerfully nilpotent groups that are finite p groups that possess a central series of a special kind to these we can attach the notion of a powerful nilpotence class that leads naturally to a classification in terms of an ancestry tree and powerful coclass we show that there are finitely many powerfully nilpotent p groups of each given powerful coclass and develop some general theory for this class of groups we also determine the growth of powerfully nilpotent groups of exponent p 2 and order p n where p is odd the number of these is f n p n 3 o n 3 where 9 4 2 394 for the larger class of all powerful groups of exponent p 2 and order p n where p is odd the number is p 2 27 n 3 o n 3 thus here the class of powerfully nilpotent p groups is large while sparse within the larger class of powerful p groups

powerful 2 engel groups ii we conclude our classification of powerful 2 engel groups of class three that are minimal in the sense that every proper powerful section is nilpotent of class at most two in the predecessor to this paper we obtained three families of minimal groups here we get a fourth family of minimal examples that is described in terms of irreducible polynomials over the field of three elements we also get one isolated minimal example of rank 5 and exponent 27 the last one has a related algebraic structure that we call a symplectic alternating algebra to each symplectic alternating algebra over the field of three elements there corresponds a unique 2 engel group of exponent 27

finite precision rational arithmetic slash number systems fraction number systems characterized by fixed slash and floating slash formats are specified the structure of arithmetic over such systems is prescribed by the rounding obtained from best rational approximation multitiered precision hierarchies of both the fixed slash and floating slash type are described and analyzed with regards to their support of both exact rational and approximate real computation

on elements of order p in powerful p groups abstract we investigate the set 1 p of elements of order at most p in a powerful p group p and prove that 1 p p p p as a corollary we obtain a necessary and sufficient condition for 1 p to be of exponent p we give an example to show that for p 2 there is a powerful 2 group such that 1 p is not of exponent 2

bounding the exponent of a finite group with automorphisms a 4 where a s a 1 this follows immediately from the fact that for every prime p dividing g there is an a invariant sylow p subgroup p of g for a which even a stronger decomposition holds p s c a see for ag a p w x example 6 theorems 6 2 2 and 6 2 4 suppose that in this situation n is the least common multiple of the exponents of the centralizers c a g a g a we show that then the exponent of g is bounded by a number that depends only on n and on the group a

characterization of p adic analytic groups in terms of wreath products abstract we show that a finitely generated pro p group is p adic analytic i e can be given the structure of a lie group over q p if and only if it does not involve arbitrarily large wreath products of the form c p wr c p n this result whose proof applies zelmanov s recent solution to the restricted burnside problem is in fact equivalent to zelmanov s theorem

fixed points of coprime operator groups abstract let m be a positive integer and a an elementary abelian group of order q r with r 2 acting on a finite q group g we show that if for some integer d such that 2 d r 1 the dth derived group of c g a has exponent dividing m for any a a then g d has m q r bounded exponent and if r 1 c g a has exponent dividing m for any a a then r 1 g has m q r bounded exponent

a classification of finite 2 groups with exactly three involutions we finish here a classification of finite 2 groups with exactly three involutions we clear up this remaining very difficult situation and determine completely the structure of g in terms of two generators and relations

fast rounding in multiprecision floating slash arithmetic a computational algorithm is described which quickly rounds large fractions into a fixed length multiprecision floating slash representation using single precision operations where possible an easily calculated criterion for terminating the rounding process is given

polynomial identities in graded group rings restricted lie algebras and p adic analytic groups let g be any finitely generated group and let k be a field of characteristic p 0 it is shown that the graded group ring gr kg satisfies a nontrivial polynomial identity if and only if the pro p completion of g is p adic analytic i e can be given the structure of a lie group over the p adic field q p the proof applies theorems of lazard quillen and passman as well as results on engel lie algebras and on dimension subgroups in positive characteristic

low power logarithmic number system addition subtraction and their impact on digital filters this paper presents techniques for low power addition subtraction in the logarithmic number system lns and quantifies their impact on digital filter vlsi implementation the impact of partitioning the look up tables required for lns addition subtraction on complexity performance and power dissipation of the corresponding circuits is quantified two design parameters are exploited to minimize complexity namely the lns base and the organization of the lns word a roundoff noise model is used to demonstrate the impact of base and word length on the signal to noise ratio of the output of finite impulse response fir filters in addition techniques for the low power implementation of an lns multiply accumulate mac units are investigated furthermore it is shown that the proposed techniques can be extended to cotransformation based circuits that employ interpolators the results are demonstrated by evaluating the power dissipation complexity and performance of several fir filter configurations comprising one two or four mac units simulations of placed and routed vlsi lns based digital filters using a 90 nm 1 0 v cmos standard cell library reveal that significant power dissipation savings are possible by using optimized lns circuits at no performance penalty when compared to linear fixed point two s complement equivalents

pipelined computation of very large word length lns addition subtraction with polynomial hardware cost a novel pipelined method is proposed to compute the addition subtraction in very large word length logarithmic number system lns arithmetic digit parallel additive normalization and digit on line multiplicative normalization methods are adopted to compute the exponential and logarithmic functions respectively in lns addition subtraction these two methods can both be implemented in a pipelined and regular architecture the size of the required lookup tables is now proportional to a third order polynomial function instead of an exponential function of the word length the total size of the tables in a 32 bit lns unit is estimated to be less than 53 5 kbits and the total size of the table s in a 64 bit lns unit will be less than 471 kbits furthermore the hardware cost of the other circuits in the proposed lns unit is only proportional to the square of the word length this study also develops a simple leading zero bits prediction technique that can significantly enhance the precision in lns addition subtraction computation when compared to floating point arithmetic design our approach still suffers from large hardware cost and pipeline latency however the proposed approach has provided a theoretical advancement in the development of very large word length lns arithmetic

dimension subgroups nilpotency indices and the number of generators of ideals in p group algebras abstract various problems in modular p group algebras are solved through extensive study of dimension subgroups as an application it is shown that if g is an infinite res p group p 2 and k is a field of characteristic p then the least upper bound on the numbers of generators of ideals in kg equals the minimal index of a cyclic subgroup of g

locally finite groups with all subgroups normal by finite rank abstract a group is said to have finite special rank sif all of its finitely generated subgroups can be generated byselements letgbe a locally finite group and suppose thath hghas finite rank for all subgroupshofg wherehgdenotes the normal core ofhing we prove that thenghas an abelian normal subgroup whose quotient is of finite rank theorem 5 if in addition there is a finite numberrbounding all of the ranks ofh hg thenghas an abelian subgroup whose quotient is of finite rank bounded in terms ofronly theorem 4 these results are based on analogous theorems on locally finitep groups in which case the groupgis also abelian by finite theorems 2 and 3

extension of a schur theorem to groups with a central factor with a bounded section rank abstract a well known result reported by schur states that the derived subgroup of a group is finite provided its central factor is finite here we show that if the p section rank of the central factor of a locally generalized radical group is bounded then so is the p section rank of its derived subgroup we also give an explicit expression for this bound

the cochlear frequency map for the cat labeling auditory nerve fibers of known characteristic frequency iontophoresis of horseradish peroxidase was used to label single auditory nerve fibers after determination of threshold tuning curves and rates of spontaneous discharge the relation between characteristic frequency cf and cochlear longitudinal location is reconstructed from 52 labeled neurons in 16 cochleas the length of the organ of corti alotted to an octave of stimulus frequency increases steadily from low to high frequencies thus there is not a simple linear distance to log frequency conversion when comparing cochleas of different total length the best predictor of cf at a given location is the distance from base or apex expressed as a percentage of the total length the cochlear frequency map derived from these single neuron labeling experiments is compared to maps derived by a number of different physiological and psychophysical techniques and the significance of the similarities and differences is discussed

applying features of ieee 754 to sign logarithm arithmetic various features found in standard floating point arithmetic ieee 754 are examined in light of their appropriateness for sign logarithm arithmetic the emphasis is on a 32 b word size comparable to ieee 754 single precision although other word sizes are possible a multilayer sign logarithm format is considered the lowest layer similar to previous implementations would provide only normalized representations but would not provide representations for zero denormalized values infinities and nans the highest layer would provide most of the features found in ieee 754 including zeros denormalized values infinities and nans novel algorithms for implementing logarithmic denormalized arithmetic are presented simulation results show that the error characteristics of the proposed logarithmic denormalized arithmetic algorithms are similar to those of the denormalized floating point arithmetic in ieee 754

on the growth of subalgebras in lie p algebras abstract let l be a finitely generated lie p algebra over a finite field f then the number a n l of p subalgebras of finite codimension n in l is finite we say that l has psg polynomial p subalgebras growth if the growth of a n l is bounded above by some polynomial in f n we show that if l has psg then the lower central series of l stabilises after a finite number of steps on the other hand if l is nilpotent then l has psg we deduce the following group theoretic result let g be a group and let g p denote a pro p completion of g then the associated lie p algebra l p g of g has psg if and only if g p is a p adic analytic lie group

arithmetic co transformations in the real and complex logarithmic number systems the real logarithmic number system which represents a value with a sign bit and a quantized logarithm can be generalized to create the complex logarithmic number system which replaces the sign bit with a quantized angle in a log polar coordinate system although multiplication and related operations are easy in both real and complex systems addition and subtraction are hard especially when interpolation is used to implement the system both real and complex logarithmic arithmetic benefit from the use of co transformation which converts an addition or subtraction from a region where interpolation is expensive to a region where it is easier two co transformations that accomplish this goal are introduced the first is an approximation based on real analysis of the subtraction logarithm the second is based on simple algebra that applies for both real and complex values and that works for both addition and subtraction

on the structure of normal subgroups of potent p groups abstract let g be a finite p group satisfying g g g4 for p 2 and p 1 g gp for p 2 the main goal of this paper is to show that any normal subgroup n of g lying in g2 is power abelian that is the following holds 1 npk gpk g n 2 k n g n o g p k and 3 n p k n k n

beauville structures in finite p groups abstract we study the existence of unmixed beauville structures in finite p groups where p is a prime first of all we extend catanese s characterisation of abelian beauville groups to finite p groups satisfying certain conditions which are much weaker than commutativity this result applies to all known families of p groups with a good behaviour with respect to powers regular p groups powerful p groups and more generally potent p groups and generalised p central p groups in particular our characterisation holds for all p groups of order at most p p which allows us to determine the exact number of beauville groups of order p 5 for p 5 and of order p 6 for p 7 on the other hand we determine which quotients of the nottingham group over f p are beauville groups for an odd prime p as a consequence we give the first explicit infinite family of beauville 3 groups and we show that there are beauville 3 groups of order 3 n for every n 5

groups satisfying semigroup laws and nilpotent by burnside varieties abstract we investigate the structure of groups satisfying apositive law that is an identity of the formu v whereuandvare positive words the main question here is whether all such groups are nilpotent by finite exponent we answer this question affirmatively for a large class c of groups including soluble and residually finite groups showing that moreover the nilpotency class and the finite exponent in question are bounded solely in terms of the length of the positive law it follows in particular that if a variety of groups is locally nilpotent by finite then it must in fact be contained in the product of a nilpotent variety by a locally finite variety of finite exponent we deduce various other corollaries for instance that a torsion free residually finite n engel group is nilpotent of class bounded in terms ofn we also consider incidentally a question of bergman as to whether a positive law holding in a generating subsemigroup of a group must in fact be a law in the whole group showing that it has an affirmative answer for soluble groups

sign logarithm arithmetic for fft implementation sign logarithm arithmetic is applicable to a variety of numerical applications where wide dynamic range and small wordsize are required in this paper the basic sign logarithm arithmetic operations required for signal processing i e addition subtraction and multiplication are reviewed the computational errors are analyzed for fft realization and simulation results are presented which serve to verify the analysis it is shown that the sign logarithm approach provides improved arithmetic quantization error performance for a given word size over fft s implemented with conventional fixed or floating point arithmetic and that the sign logarithm implementation is faster and less complex than conventional approaches

duration sensation in relation to the autocorrelation function of sound stimuli relationships were investigated between subjective judgment of physical duration and the factors extracted from the autocorrelation function acf of sound stimuli factors of acf were changed by using different properties of pure tone complex tone white noise and bandpass noise stimuli experiments by paired comparison method were conducted in the sound proof chamber except for one in a concert hall sound stimuli were selected on the basis of the measured factors of acf as parameters subjects were asked to compare the durations of two stimuli in the pair subjective durations were obtained in the psychometric function and were interpreted as duration sensation ds on the basis of the auditory brain model and the theory of primary sensation results p 0 05 are shown as below 1 dss are longer with larger 1 being time delay of first peak of acf corresponding to pitch 2 dss are longer with higher 0 being energy at the beginning of acf 3 dss are longer with smaller m being constant am

interleaved memory function interpolators with application to an accurate lns arithmetic unit this paper describes a new method for polynomial interpolation in hardware with advantages demonstrated by its application to an accurate logarithmic number system lns arithmetic unit the use of an interleaved memory reduces storage requirements by allowing each stored function value to be used in interpolation across several segments this strategy can be shown to always use fewer words of memory than an optimized polynomial with stored polynomial coefficients interleaved memory function interpolators are then applied to the specific goal of an accurate logarithmic number system arithmetic unit many accuracy requirements for the lns arithmetic unit are possible although a round to nearest would be desirable it cannot be easily achieved the goal suggested is to insure that the worst case lns relative error is smaller than the worst case floating point fp relative error using the interleaved memory interpolator the detailed design of an lns arithmetic unit is performed using a second order polynomial interpolator including approximately 91k bits of rom this arithmetic unit has better accuracy and less complexity than previous lns units

asymptotic results for primitive permutation groups abstract we prove that the number of conjugacy classes of primitive permutation groups of degreenis at mostnc n where n denotes the maximal exponent occurring in the prime factorization ofn this result is applied to investigating maximal subgroup growth of infinite groups we then proceed by showing that if the point stabilizerg of a primitive groupgof degreendoes not have the alternating group alt d as a section then the order ofgis bounded by a polynomial inn this result extends a well known theorem of babai cameron and palfy it is used to prove for example that ifhis a subgroup of indexnin a groupg andhis a product ofbcyclic groups then g hg ncwherecdepends onb

robust transmission of unbounded strings using fibonacci representations families of fibonacci codes and fibonacci representations are defined their main attributes are robustness manifesting itself by the local containment of errors and simple encoding and decoding the main application explored is the transmission of binary strings in which the length is in an unknown range using robust fibonacci representations instead of the conventional error sensitive logarithmic ramp representation though the former is asymptotically longer than the latter the former is actually shorter for very large initial segments of integers

semi logarithmic number systems we present a new class of number systems called semi logarithmic number systems that constitute a family of various compromises between floating point and logarithmic number systems this allows trade between the speed of the arithmetic operations and the size of the required tables we give arithmetic algorithms addition subtraction multiplication division for the semi logarithmic number systems and we compare these number systems to the classical floating point or logarithmic number systems