further results on morgan s problem this paper deals with the row by row decoupling problem known as the morgan problem with static state feedback the solution of this problem is well known when some artificial constraints on the feedback laws are imposed such as regular input transformations or restricted state feedbacks however in its most general setting the problem remains unsolved we provide here a new sufficient condition of its solvability the fact that this condition turns out to be also necessary in the particular case of systems having 2 outputs and 3 inputs enforces its interest

the influence of ss quasinormality of some subgroups on the structure of finite groups the following concept is introduced a subgroup h of the group g is said to be ss quasinormal supplement sylow quasinormal in g if h possesses a supplement b such that h permutes with every sylow subgroup of b groups with certain ss quasinormal subgroups of prime power order are studied for example fix a prime divisor p of g and a sylow p subgroup p of g let d be the smallest generator number of p and md p denote a family of maximal subgroups p1 pd of p satisfying i 1d pi p the frattini subgroup of p assume that the group g is p solvable and every member of some fixed md p is ss quasinormal in g then g is p supersolvable

almost invariant subspaces an approach to high gain feedback design part ii almost conditionally invariant subspaces in part i of this paper almost controlled invariant subspaces were studied in this part we will consider their duals the almost conditionally invariant subspaces these concepts give immediately by dualization of the almost disturbance decoupling control by state feedback the solution of the almost disturbance decoupled estimation problem finally we consider the problem of approximate disturbance decoupling by measurement feedback and it is shown that this problem is solvable to any arbitrary degree of accuracy if and only if 1 almost disturbance decoupling by state feedback and 2 almost disturbance decoupled estimation of the to be controlled output are both possible

the solution of diagonal decoupling problem by dynamic output feedback and constant precompensator the general case in this paper the solution to diagonal decoupling problem via dynamic output feedback and constant precompensator is presented in the general case the literature contains a number of particular solutions for this problem these solutions are valid for instance for square transfer matrices or they employ restricted dynamic output feedback schemes here we start with a nonsquare transfer matrix and consider a dynamic output feedback scheme where there is a proper compensator in the feedback loop accompanied by a constant gain precompensator in the feedforward path in this respect the problem being considered is the dynamic output feedback version of the well known morgan s problem the approach taken involves the characterization of open loop diagonalizers which admit a dynamic output feedback realization the key concepts involved in the solution are the generalized version of diagonal causality degree dominance and the set of attainable infinite zero orders an example is also included to illustrate the main result

on σ subnormal and σ permutable subgroups of finite groups let i i i be some partition of the set p of all primes that is p i i i and i j for all i j let g be a finite group we say that g is primary if g is a i group for some i i soluble if every chief factor of g is primary we say that a set h h1 ht of hall subgroups of g where hi is primary i 1 t is a complete hall set of type of g if hi hj 1 for all i j and g h1 ht we say that a subgroup a of g is subnormal in g if there is a subgroup chain a a0 a1 an g such that either ai 1 is normal in ai or ai ai 1 ai is primary for all i 1 t permutable in g if g has a complete hall set h of type such that a is hg permutable in g that is ahx hxa for all x g and all h h we study the relationship between the subnormal and permutable subgroups of g in particular we prove that every permutable subgroup of g is subnormal and we classify finite soluble groups in which every subnormal subgroup is permutable

permutable products of supersoluble groups we investigate the structure of finite groups that are the mutually permutable product of two supersoluble groups we show that the supersoluble residual is nilpotent and the fitting quotient group is metabelian these results are consequences of our main theorem which states that such a product is supersoluble when the intersection of the two factors is core free in the group

generating directional residuals with dynamic parity relations abstract it is shown how diagnostic residuals which exhibit directional properties at all times in response to an arbitrary mix of input and output faults can be generated using dynamic parity relations the parity relations are applied directly to the observables of the monitored plant the design relies on the plant s dynamic input output model this residual generator can be made computationally polynomial moving average by including the invariant zero polynomial of the fault system in the specified fault responses the polynomial design yields moving average noise transfers as well white noise transfer and disturbance decoupling are achieved by extending the response specification the parity relation approach is compared with the traditional detection filter design and is shown to be more straightforward and have milder existence conditions if subjected to the same specification the two approaches yield identical residual generators

a new interpretation of the fault detection filter part 1 closed form algorithm a novel interpretation is presented of the detection filter in the context of an eigenstructure assignment problem the detection filter is shown to be equivalent to the combination of two decoupled observers with the advantage that theories already developed for conventional observers can be utilized as design aids detection space and detection order are re defined accordingly and it is shown that of the two observers that constitute a detection filter the one associated with the detection space is a single output system this fact is important since it explains important properties of the fault detection filter in a very uncomplicated fashion leading to a clear interpretation of the freedom available in designing the filter in particular it is proven that the detection filter gains are unique given the eigenvalues of the detection space further the formulation leads to a closed form expression for the detection filter and is therefore well suited to the development of simple design algorithms

some new characterizations of pst groups abstract let h and b be subgroups of a finite group g such that g n g h b then we say that h is quasipermutable respectively s quasipermutable in g provided h permutes with b and with every subgroup respectively with every sylow subgroup a of b such that h a 1 in this paper we analyze the influence of s quasipermutable and quasipermutable subgroups on the structure of g as an application we give new characterizations of soluble pst groups

2d residual generation and dead beat observers abstract in this paper we consider the 2d residual generation problem in an algebraic context an algorithmic method that provides a complete family of residual generators is presented and some connections between 2d residual generation and 2d dead beat observer synthesis are investigated

invariant subspaces for lpv systems and their applications the aim of this paper is to extend the notion of invariant subspaces known in the geometric control theory of the linear time invariant systems to the linear parameter varying lpv systems by introducing the concept of parameter varying invariant subspaces for lpv systems affine in their parameters algorithms are given to compute many parameter varying subspaces relevant in the solution of state feedback and observer design problems

a criterion of p hypercyclically embedded subgroups of finite groups abstract let g be a finite group e a normal subgroup of g and p a fixed prime we say that e is p hypercyclically embedded in g if every p g chief factor of e is cyclic a subgroup h of g is said to satisfy property in g if g k n g k h l k k is a h l k k number for any chief factor l k in g h is said to be normal in g if g has a subnormal supplement t of h such that h t i h for some subgroup i satisfying property in g in this paper we prove that e is p hypercyclically embedded in g if and only if some classes of p subgroups of e are normal in g many recent results are extended

a solution to the diagonalization problem by constant precompensator and dynamic output feedback a solution is presented for the problem of diagonalization row by row decoupling the problem is solved using a constant precompensator and a dynamic output feedback compensator of a p m linear time invariant system the solvability condition is compact and concerns the dimension of a single subspace defined via the concepts of essential rows and static kernels associated with the transfer matrix a characterization of the set of all solutions to the problem is also given in solving this dynamic feedback problem a complete solution to its state feedback counterpart namely the restricted state feedback problem of diagonalization is also presented

finite groups with subgroups supersoluble or subnormal abstract the aim of this paper is to study the structure of finite groups whose non subnormal subgroups lie in some subclasses of the class of finite supersoluble groups

totally permutable products of certain classes of finite groups abstract subgroups a and b of a finite group are said to be totally permutable if every subgroup of a permutes with every subgroup of b the behaviour of finite pairwise totally permutable products are studied with respect to certain classes of groups including the class of groups where all the subnormal subgroups permute with all the maximal subgroups the so called sm groups and also the class of groups where all the subnormal subgroups are permutable the so called pt groups

x semipermutable subgroups of finite groups abstract let x be a non empty subset of a group g then we call a subgroup a of g a x semipermutable subgroup of g if a has a supplement t in g such that for every subgroup t 1 of t there exists an element x x such that a t 1 x t 1 x a in this paper we study the properties of x semipermutable subgroups in particular a new version of the famous schur zassenhaus theorem in terms of x semipermutable subgroups is given

instantaneous and finite time blow up of solutions to a reaction diffusion equation with hardy type singular potential abstract we deal with radially symmetric solutions to the reaction diffusion equation with hardy type singular potential u t u m k x 2 u m posed in r n 0 t in dimension n 3 where m 1 and 0 k n 2 2 4 we prove that in dependence of the initial condition u 0 l r n c r n its solutions may either blow up instantaneously or blow up in finite time at the origin thus developing a singularity at x 0 but they can be continued globally in weak sense the instantaneous blow up occurs for example for any data u 0 such that u 0 0 0 the proofs are based on a transformation mapping solutions to our equation into solutions to a non homogeneous porous medium equation

on some classes of supersoluble groups finite groups g for which for every subgroup h and for all primes q dividing the index g h there exists a subgroup k of g such that h is contained in k and k h q are called y groups groups in which subnormal subgroups permute with all sylow subgroups are called pst groups in this paper a local version of the y property leading to a local characterisation of y groups from which the classical characterisation emerges is introduced the relationship between pst groups and y groups is also analysed

a geometric approach to the synthesis of failure detection filters a geometric formulation of beard s failure detection filter problem is stated using the concepts of c a invariant and unobservability subspaces the notions of output separable and mutually detectable families of subspaces introduced by beard are also clarified it is shown that mutual detectability is a necessary and sufficient condition for the existence of a detection filter with arbitrarily assignable spectrum moreover it is shown that the failure detection falter problem has a computationally simple solution when the failure events satisfy some mild restrictions finally the complete duality between a generalization of beard s detection filter problem and the restricted control decoupling problem is illustrated

on the xφ hypercentre of finite groups abstract let g be a finite group x a class of groups a chief factor h k of g is called x central provided h k g c g h k x let z x g be the product of all normal subgroups h of g such that all non frattini g chief factors of h are x central then we say that z x g is the x hypercentre of g our main result here is the following theorem 1 4 let x e be normal subgroups of a group g suppose that every non cyclic sylow subgroup p of x has a subgroup d such that 1 d p and every subgroup h of p with order h d and every cyclic subgroup of p with order 4 if d 2 and p is a non abelian 2 group is weakly s permutable in g if x is either e or f e then e z u g here u is the class of all supersoluble finite groups

solution to morgan s problem a necessary and sufficient condition is presented for the solution of the row by row decoupling problem known as morgan s problem in the general case that is without any restrictive assumption added to the system to the feedback law u fx gy g may be noninvertible this is a structural condition in terms of invariant lists of integers which are easily computable from a given state realization of the system these integers are the infinite zero orders morse s list i sub 4 and the essential orders of the system which only depend on the input output behavior and morse s list i sub 2 of the system which depends on the choice of a particular state realization

lie symmetries and form preserving transformations of reaction diffusion convection equations abstract new lie symmetry classification of the known class of reaction diffusion convection equations is presented the classification method is based on combining the standard group classification method and the form preserving transformation approach

sylow permutable subnormal subgroups of finite groups abstract an extension of the well known frobenius criterion of p nilpotence in groups with modular sylow p subgroups is proved in the paper this result is useful to get information about the classes of groups in which every subnormal subgroup is permutable and sylow permutable

solution of the static state feedback decoupling problem for linear systems with two outputs we give for linear systems with two outputs a necessary and sufficient condition for the solvability of the restricted decoupling problem rdp in terms of some structural invariants a geometric characterization is also given which provides the least dynamical extension needed when rdp is not solvable

the form of blow up for nonlinear parabolic equations on considere des equations paraboliques semi lineaires de la forme u t 2 u sf u ou f est positive et 0 ds f s est finie on etudie des problemes a 1 dimension dans la region semi infinie x o et on trouve le temps t

criteria for permutability to be transitive in finite groups abstract a group g is a pt group if for subgroups h and k with h permutable in k and k permutable in g it is always the case that h is permutable in g it is shown that a finite group is a soluble pt group if and only if each subgroup of a sylow subgroup is permutable in the sylow normalizer

on σ supersoluble groups and one generalization of clt groups abstract let g be a finite group and i i i be a partition of the set of all primes p a chief factor h k of g is said to be central in g if the semidirect product h k g c g h k is a i group for some i i the group g is said to be nilpotent if either g 1 or every chief factor of g is central let g n be the nilpotent residual of g that is the intersection of all normal subgroups n of g with nilpotent quotient g n then we say that g is supersoluble if each chief factor of g below g n is cyclic in this paper we study properties of supersoluble groups and also consider some applications of such groups in the theory of generalized clt groups

on hall subnormally embedded and generalized nilpotent groups abstract a subgroup h of a finite group g is said to be hall subnormally embedded in g if h is a hall subgroup of the subnormal closure h s g in this paper some new characterizations for finite groups are obtained based on the assumption that some subgroups are hall subnormally embedded

fault detection for linear periodic systems using a geometric approach using the geometric approach a solution is given to the problem of detecting faults in linear periodic discrete time systems the solution consists on developing an unknown input observer the existing conditions are provided in terms of new geometric notion of outer observable subspace that is the dual notion of inner reachable subspace making use of the new notion a residual generator is developed such that the residual is made independent of unknown input disturbance and its output free response goes asymptotically to zero

groups with chernikov conjugacy classes in which sylow permutability is a transitive relation a subgroup h of a periodic group g is said to be sylow permutable in g if hs sh for every sylow subgroup s of g like normality sylow permutability is not a transitive relation in this paper we characterize periodic locally soluble groups with chernikov conjugacy classes periodic locally soluble cc groups in which sylow permutability is a transitive relation pst groups describing their structure in a very detailed way then extending the structure of finite soluble pst groups moreover we give an effective construction of these groups

on totally permutable products of finite groups this paper has been published in journal of algebra 293 1 269 278 2005 copyright 2005 by elsevier http dx doi org 10 1016 j jalgebra 2005 01 033

clt groups with normal or abnormal subgroups abstract finite groups g for every divisor d of the order of g if there exists a subgroup h of g of order d such that h is normal or abnormal are called c groups in this paper c groups are characterized as certain extensions of nilpotent normal subgroups by subgroups of prime power order

well posedness of initial value problems for singular parabolic equations abstract we study well posedness of initial value problems for a class of singular quasilinear parabolic equations in one space dimension simple conditions for well posedness in the space of bounded nonnegative solutions are given which involve boundedness of solutions of some related linear stationary problems by a suitable change of unknown the above results can be applied to classical initial boundary value problems for parabolic equations with singular coefficients as the heat equation with inverse square potential

decoupling by restricted static state feedback the general case in this paper we tackle the general block decoupling problem for linear constant dynamical systems c a b with m inputs and p outputs with restricted static state feedback in other words with control laws of type u gfx gv we give a necessary and sufficient condition of existence for such laws which generalizes the one previously given in 2 for the simple case k p leq m where k denotes the number of blocks to be decoupled

on σ subnormal subgroups of factorised finite groups abstract let i i i be a partition of the set p of all prime numbers a subgroup x of a finite group g is called subnormal in g if there is chain of subgroups x x 0 x 1 x n g with x i 1 normal in x i or x i c o r e x i x i 1 is a i group for some i i 1 i n in the special case that is the partition of p into sets containing exactly one prime each the subnormality reduces to the familiar case of subnormality if a finite soluble group g a b is factorised as the product of the subgroups a and b and x is a subgroup of g such that x is subnormal in x x g for all g a b we prove that x is subnormal in g this is an extension of a subnormality criteria due to maier and sidki and casolo

decoupling by dynamic measurement feedback with stability necessary and sufficient conditions the noninteracting control problem of linear time invariant multivariable systems by dynamic measurement feedback is solved in the state space geometric approach the generalization of w m wonham s edp 1979 is considered the problem of the reduction of compensator s order is not treated but the solution derived is able to solve simultaneous problems like the decoupling and the disturbance decoupling problems

block decoupling and arbitrary pole assignment for a linear right invertible system by dynamic compensation abstract the block decoupling of a linear right invertible system by dynamic compensation is studied the system structure of the block decoupled system is clarified from the viewpoint of the closed loop poles a dynamic compensator that realizes block decoupling and arbitrary pole assignment is proposed two examples are given to illustrate the design procedure of the dynamic compensator and its effectiveness

equivalence and finite time blow up of solutions and interfaces for two nonlinear diffusion equations abstract in this work we construct a transformation between the solutions to the following reaction convection diffusion equation t u u m x x a x u m x b x u m posed for x r t 0 and m 1 where a b are two continuous real functions and the solutions to the nonhomogeneous diffusion equation of porous medium type f y m y y posed in the half line y 0 with 0 m 1 and suitable density functions f y we apply this correspondence to the case of constant coefficients a x 1 and b x k 0 for this case we prove that compactly supported solutions to the first equation blow up in finite time together with their interfaces as x we then establish the large time behavior of solutions to a homogeneous dirichlet problem associated to the first equation on a bounded interval we also prove a finite time blow up of the interfaces for compactly supported solutions to the second equation when f y y with 2

finite groups with σ subnormal schmidt subgroups abstract we study the finite groups all the schmidt subgroups the minimal non nilpotent subgroups of which are subnormal thus an affirmative answer is obtained to problem 19 85 from the kourovka notebook

a general approach to the eigenstructure assignment for reachability and stabilizability subspaces abstract this paper is concerned with the problem of determining basis matrices for the supremal output nulling reachability and stabilizability subspaces and the simultaneous computation of the associated friends that place the assignable closed loop eigenvalues at desired locations our aim is to show that the moore laub algorithm in moore and laub 1978 for the computation of these subspaces was stated under unnecessary restrictive assumptions we prove the same result under virtually no system theoretic hypotheses this provides a theoretical foundation to a range of recent geometric techniques that are more efficient and robust and as general as the standard ones based on the computation of sequences of subspaces

on σ local fitting classes abstract let be a partition of the set of all primes p if g is a finite group and f is a fitting class of finite groups the symbol g denotes the set i i g and f f g we call any function f of the form f fitting classes a hartley function or simply h function and we put l r f g g 1 or g 1 and g g i g i f i for all i g if there is an h function f such that f l r f then we say that f is local and f is a local definition of f in this paper we describe some properties of local fitting classes and prove that 1 every local fitting class can be defined by a unique h function f such that f i f i g i f and f i is a lockett class for all i f 2 the product of two local fitting classes is also a local fitting class moreover we also discuss the n multiply local fitting classes

group classes and mutually permutable products abstract let g a b be the mutually permutable product of the nontrivial subgroups a and b of the group g then a or b contains a nontrivial normal subgroup of g it is also established that s g a s a where s u is the solvable radical of u these facts lead to some generalized results about mutually permutable products of sc groups it is also shown that if g is a pts group then a and b are pst groups

decoupling of square singular systems via proportional state feedback necessary and sufficient conditions for the decoupling of a solvable square singular system ex t ax t bu t with output y t dx t through an admissible control law of the form u t kx t hr t where h is a square nonsingular matrix it has been shown that for a given singular system that satisfies these conditions a propagational state feedback exists for which the system s transfer function is a diagonal nonsingular and proper rational matrix the proofs of the main results are constructive and provide a procedure for computing an appropriate proportional state feedback

a game theoretic fault detection filter the fault detection process is approximated with a disturbance attenuation problem the solution to this problem for both linear time varying and time invariant systems leads to a game theoretic filter which bounds the transmission of all exogenous signals except the fault to be detected in the limit when the disturbance attenuation bound is brought to zero a complete transmission block is achieved by embedding the nuisance inputs into an unobservable invariant subspace since this is the same invariant subspace structure seen in some types of detection filters we can claim that the asymptotic game filter is itself a detection filter one can also make use of this subspace structure to reduce the order of the limiting game theoretic filter by factoring this invariant subspace out of the state space the resulting lower dimensional filter will then be sensitive only to the failure to be detected a pair of examples given at the end of the paper demonstrate the effectiveness of the filter for time invariant and time varying problems in both full order and reduced order forms

the generalized eigenstructure problem in linear system theory the algebraic theory of linear time invariant systems has been studied in large detail during the past few decades and numerous computational algorithms have been developed to solve problems arising in this context in this paper the numerical aspects of a certain class of such algorithms dealing with what the author calls generalized eigenstructure problems are discussed some new and or modified algorithms are presented both the nmnerical stability of the algorithms and the conditioning of the problems they solve are analyzed using numerical criteria

computation of the structural invariants of linear multivariable systems with an extended version of the program zeros abstract the structural invariants like finite and infinite zeros play an important role in many problems in the analysis of linear systems in 1 emami naeini and van dooren presented the program zeros for computing the finite zeros of a linear system which in the author s opinion is at present the best commonly available program for this problem such a program does not exist for computing the other structural invariants like the infinite zeros and the kronecker indices this paper presents an extended version of the program zeros which computes the finite zeros as well as the other structural invariants

the block essential orders and the dynamic block decoupling problem abstract in recent papers 8 it has been pointed out that two invariant lists of integers the infinite zero orders and the essential orders play a key role in the solution of the so called morgan s problem i e the row by row decoupling problem the purpose of the present paper is to define the block essential orders of a linear system with respect to the block decoupling problem this is done through a new dynamic solution to the latter based upon a procedure which extends to the block case that previously given in 15 for morgan s problem this procedure is minimal in the sense that it leads to the least infinite zero structure for any decoupled system reachable from the original one

optimal stochastic fault detection filter a fault detection and identification algorithm called optimal stochastic fault detection filter is determined the objective of the filter is to detect a single fault called the target fault and block other faults called the nuisance faults in the presence of the process and sensor noises the filter is derived by maximizing the transmission from the target fault to the projected output error while minimizing the transmission from the nuisance faults therefore the residual is affected primarily by the target fault and minimally by the nuisance faults the transmission from the process and sensor noises is also minimized so that the filter is robust with respect to these disturbances it is shown that the filter recovers the geometric structure of the unknown input observer in the limit where the weighting on the nuisance fault transmission goes to infinity further the asymptotic behavior of the filter near the limit is determined by using a perturbation method filter designs can be obtained for both time invariant and time varying systems

fault detection in a mixed h sub 2 h sub spl infin setting in this note we study the problem of fault detection in linear time invariant lti systems which are simultaneously effected by two classes of unknown inputs noises having fixed spectral densities and unknown finite energy disturbances this problem is formulated as a mixed h sub 2 h sub spl infin filtering problem necessary and sufficient conditions for local optimality are presented moreover it is shown that suboptimal solutions can be computed by solving a convex minimization problem with a set of linear matrix inequality lmi constrains a numerical example is given to illustrate the advantage of the mixed h sub 2 h sub spl infin approach as compared to existing techniques which are based on optimization of h sub 2 and h sub spl infin criteria

on fφ hypercentral subgroups of finite groups let g be a finite group we write r g to denote the largest soluble normal subgroup of g and put g r g we say that a chief factor h k of g is non frattini non solubly frattini if h k g k if h k g k respectively a chief factor h k of g is called f central in g provided h k g cg h k f a normal subgroup n of g is said to be f hypercentral f hypercentral in g if either n 1 or n 1 and there exists a chief series 1 n0 n1 nt n of g below n such that every non frattini non solubly frattini respectively factor ni ni 1 of series is f central in g in this paper we analyze some properties and applications of f hypercentral and f hypercentral subgroups

solvable pst groups strong sylow bases and mutually permutable products article history as ubgrouph of a group g is said to permute with the subgroup k of g if hk kh s ubgroupsh and k are mutually permutable totally permutable i ng if every subgroup of h permutes with k and every subgroup of k permutes with h if every subgroup

global travelling waves in reaction convection diffusion equations we study the existence and properties of solutions in travelling wave form u x t x st defined for every z x st r for the reaction convection diffusion equationut a um xx b un x kupforx r t 0 with a m n 0 b k p r in the reaction case k 0 we prove that there exist travelling waves vanishing for z if and only if b 0 and min 1 n m p2 max 1 n p max 1 n moreover if m p 2n there exists a minimal velocity s a b k m n p 0 for which there are travelling waves only with s s while in the case m p 2n there are travelling waves only when 4amk b2n and for every velocity s 0 some properties of the function s are established all the waves are decreasing in their support and waves having bounded support from the right exist if and only if m min 1 n also the absorption case k 0 is treated where we find that for different values of the parameters there exists a unique travelling wave for every velocity s r but for some case where only negative velocities exist the cases b 0 or k 0 are well known in the literature

finite groups with given s embedded and n embedded subgroups abstract let g be a finite group and h a subgroup of g then h is said to be s permutable in g if h p p h for all sylow subgroups p of g let h s g be the subgroup of h generated by all those subgroups of h which are s permutable in g and h s g the intersection of all such s permutable subgroups of g which contain h we say that 1 h is s embedded in g if g has an s permutable subgroup t such that t h h s g and h t h s g 2 h is n embedded in g if g has a normal subgroup t such that t h h s g and h t h g our main results here are the following theorems theorem a a group g is supersoluble if and only if every maximal subgroup of every non cyclic sylow subgroup of the generalized fitting subgroup f g of g is n embedded in g theorem b a group g is supersoluble if and only if for every non cyclic sylow subgroup p of the generalized fitting subgroup f g of g every cyclic subgroup h of p with prime order and with order 4 if p is a non abelian 2 group and h z g is n embedded in g theorem f a group g is supersoluble if and only if every 2 maximal subgroup e of g with non primary index g e both has a cyclic supplement in e s g and is s embedded in g

some characterizations of finite σ soluble pσt groups abstract let i i i be some partition of the set of all primes p and g a finite group g is said to be soluble if every chief factor h k of g is a i group for some i i h k a set h of subgroups of g is said to be a complete hall set of g if every member 1 of h is a hall i subgroup of g for some i and h contains exactly one hall i subgroup of g for every i i such that i g a subgroup a of g is said to be permutable in g if g has a complete hall set h such that a h x h x a for all x g and all h h we obtain characterizations of finite soluble groups g in which permutability is a transitive relation in g

block noninteracting control with non regular static state feedback a complete solution abstract we consider linear time invariant systems c a b where the output map c is partitioned into k blocks c i we assume that the system are block right invertible i e the rank of c a b equals the sum of the ranks of the subsystems c i a b we give for the first time a necessary and sufficient condition for the solution of the block decoupling problem using static state feedbacks of the type u fx gv with g possibly nonregular for solving the decoupling problem we impose that the rank of the closed loop system equals that of c a b this is a structural condition in terms of invariant lists of integers the infinite zero orders the block essential orders and morse s list i 2 of c a b the main result theorem 3 generalizes that of our previous work for the so called morgan s problem i e the row by row decoupling problem

on the structure at infinity of linear block decouplable systems the general case the aim of this note is to show that a linear system c a b is block decouplable by means of static state feedback laws f g with g invertible if and only if the infinite structure of c a b equals the union of the infinite structures of the subsystems c i a b extracted from the given output partition this result generalizes the ones recently obtained for morgan s problem 6 and for the particular cases of right invertible 7 or left invertibie 8 systems

geometric aspects of reduced order compensators for disturbance rejection the disturbance decoupling problem with stability constraint and pole placement is examined in a geometric framework two types of reduced order compensators are proposed one based on the observation scheme the other on the dual observation scheme the novelty lies mainly in these points 1 the avoidance of eigenspace computations in the syntheses as they rely on the determination of the maximum controlled invariant contained in a given subspace and its dual i e the minimum conditioned invariant containing a given subspace and pole assignability and 2 the concerted use of controlled and conditioned invariants which leads to a straightforward synthesis and also allows a clear interpretation of the dual compensation

subgroups permutable with all sylow subgroups fix a finite group g whenever s is a nonempty set of subgroups of g let sh denote the set of all subgroups h of g permutable with all s g s h so that the complex product hs s sh is their join it is obvious that s is closed with respect to joins in case s s syl g is the set of all sylow subgroups of g for all primes it is also closed with respect to intersec w x h tions kegel 4 so that syl g is a lattice the present paper may be seen as continuation of kegel s work to be more precise it aims to continue the first part of his work the second one being completed by w x kleidman 5 h syl g is the full subgroup lattice of g precisely when g g n is nilpotent the formation n of nilpotent groups will play a central role in general as usual we denote by g the nilpotent residual of g for subgroups h and k of g we write h s f h x and h k s k x g k 2 x x h x g k for the k core and the k closure of h respectively h s y1 x hx h k h suppose h g syl g then h and h do belong to syl g for all k n k but h usually does not nor does it the commutator group h9 nor the centre z h on the other hand we know that there is a unique subgroup of h minimal subject to containing h n and belonging to h syl g this is always a normal subgroup of g

on mutually permutable products of finite groups abstract in this paper a structural theorem about mutually permutable products of finite groups is obtained this result is used to derive some results on mutually permutable products of groups whose chief factors are simple some earlier results on mutually permutable products of supersoluble groups appear as particular cases

on sublattices of the subgroup lattice defined by formation fitting sets abstract throughout this paper g always denotes a group and l g is the lattice of all subgroups of g if k h g then h k is called a section of g such a section is called normal if k h g we call any set of normal sections of g a stratification of g provided i is g closed that is h k whenever h k g t l and ii l k h l for each triple k l h where h k and l g now let be any stratification of g then we write l g to denote the set of all subgroups a of g such that a g a g we say that a stratification of g is a formation fitting set of g provided i h k n for every two sections h k h n and ii h v k for every two sections h k v k we prove that the set l g forms a sublattice of l g for every formation fitting set of g and we also discuss some applications of sublattices of this kind

an eigenstructure assignment algorithm for the design of fault detection filters in this paper we present an algorithm for the construction of detection spaces in a fault detection filter by direct eigenstructure assignment the algorithm permits great flexibility and simplifies the process of designing fault detection filters

control systems analysis for the fornasini marchesini 2d systems model progress after four decades the development of a control systems theory for multidimensional linear systems i e systems with more than one independent variable is an area where a very significant volume of research is based

new decoupling invariants the essential orders the aim of this paper is to introduce a new list of integers which is invariant under the action of biproper compensation and which plays a key role in the solution of the row by row decoupling problem several equivalent characterizations are provided within both the geometric and the transfer matrix approaches

extensions with overlap abstract let n be a normal subgroup of the group g by a result of p hall g is nilpotent if n and g n are nilpotent we are looking for group classes c and characteristic subgroups f n of n such that the statement above with belongs to c f n substituted for is nilpotent n remains true

large time behavior for a porous medium equation in a nonhomogeneous medium with critical density abstract we study the large time behavior of solutions to the cauchy problem for the porous medium equation in nonhomogeneous media with critical singular density x 2 t u u m in r n 0 where m 1 and n 3 with nonnegative initial condition u x 0 u 0 x 0 the asymptotic behavior proves to have some interesting and striking properties we show that there are different asymptotic profiles for the solutions depending on whether the continuous initial data u 0 vanishes at x 0 or not moreover when u 0 0 0 we show the convergence towards a peak type profile presenting a jump discontinuity coming from an interesting asymptotic simplification to a conservation law while when u 0 0 0 the limit profile remains continuous these phenomena illustrate the strong effect of the singularity at x 0 we improve the time scale of the convergence in sets avoiding the singularity on the way we also study the large time behavior for a porous medium equation with convection which is interesting for itself

asymptotic behavior for the critical nonhomogeneous porous medium equation in low dimensions abstract we deal with the large time behavior for a porous medium equation posed in nonhomogeneous media with singular critical density x 2 t u x t u m x t x t r n 0 m 1 posed in dimensions n 1 and n 2 which are also interesting in applied models according to works by kamin and rosenau we deal with the cauchy problem with bounded and continuous initial data u 0 we show that in dimension n 2 the asymptotic profiles are self similar solutions that vary depending on whether u 0 0 0 or u 0 0 k 0 in dimension n 1 things are strikingly different and we find new asymptotic profiles of an unusual mixture between self similar and traveling wave forms we thus complete the study performed in previous recent works for the higher dimensions n 3

on blow up at space infinity for semilinear heat equations abstract a nonnegative blowing up solution of the semilinear heat equation u t u u p with p 1 is considered when initial data u 0 satisfies lim x u 0 m 0 u 0 m and u 0 m it is shown that the solution blows up only at space infinity and that lim x u x t is the solution of the ordinary differential equation v t v p with v 0 m

finite soluble groups with permutable subnormal subgroups abstract a finite group g is said to be a pst group if every subnormal subgroup of g permutes with every sylow subgroup of g we shall discuss the normal structure of soluble pst groups mainly defining a local version of this concept a deep study of the local structure turns out to be crucial for obtaining information about the global property moreover a new approach to soluble pt groups i e soluble groups in which permutability is a transitive relation follows naturally from our vision of pst groups our techniques and results provide a unified point of view for t groups pt groups and pst groups in the soluble universe showing that the difference between these classes is quite simply their sylow structure

on weakly s permutable subgroups of finite groups abstract let g be a finite group h a subgroup of g and h s g the subgroup of h generated by all those subgroups of h which are s permutable in g then we say that h is weakly s permutable in g if g has a subnormal subgroup t such that h t g and t h h s g we fix in every non cyclic sylow subgroup p of g a subgroup d satisfying 1 d p and study the structure of g under the assumption that all subgroups h with h d are weakly s permutable in g

some permutability properties related to f hypercentrally embedded subgroups of finite groups let f denote a saturated formation in this paper we study some properties of f hypercentrally embedded subgroups i e those subgroups t of a finite group g such that every chief factor of g between its core and its normal closure is f central in g we prove that these subgroups form a sublattice of the lattice of all subgroups of g i ff is subgroup closed the main result of the paper is the following if f contains the class of nilpotent groups and g is a soluble group a subgroup t which permutes with all sylow subgroups of g is f hypercentrally embedded in g if and only if t permutes with some f normalizer of g 2003 elsevier science usa all rights reserved

some classes of finite groups and mutually permutable products this paper has been published in journal of algebra 319 8 3343 3351 2008 copyright 2008 by elsevier http dx doi org 10 1016 j jalgebra 2007 12 001

generalised norms in finite soluble groups abstract we give a framework for a number of generalisations of baer s norm that have appeared recently for a class c of finite nilpotent groups we define the c norm c g of a finite group g to be the intersection of the normalisers of the subgroups of g that are not in c we show that those groups for which the c norm is not hypercentral have a very restricted structure the non nilpotent groups g for which g c g have been classified for some classes we give a classification for nilpotent classes closed under subgroups quotients and direct products of groups of coprime order and show the known classifications can be deduced from our classification

geometric tools for solving the fdi problem for linear periodic discrete time systems this paper studies the problem of detecting and isolating faults in linear periodic discrete time systems the aim is to design an observer based residual generator where each residual is sensitive to one fault whilst remaining insensitive to the other faults that can affect the system making use of the geometric tools and in particular of the outer observable subspace notion the fault detection and isolation fdi problem is formulated and necessary and solvability conditions are given an algorithmic procedure is described to determine the solution of the fdi problem

brief generic solvability of the failure detection and identification problem necessary and sufficient conditions for the generic solvability of the extended fundamental problem in residual generation efprg massoumnia et al 1989 ieee trans automat control 34 316 321 in the case of simultaneous actuator and sensor failures are presented in the process of deriving these conditions the generic forms of supremal controllability and infimal unobservability subspaces of lti systems having diagonal state space matrices are obtained