regular orbits on symplectic modules let g be a finite group and let v be a faithful kg module k a field the question is does v contain a regular g orbit the problem has been widely studied in the literature in l berger proves that the answer is positive when a is nilpotent c 1 c free for every p and char k 1 a in 6 hargraves drops the condition of being a c c free for odd primes which are not mersenne primes a simplified proof of the main results of hargraves may be found in fleischmann s paper 3 in s gow shows that the conclusion holds when a is nilpotent char k j j a 1 and both 1 a i and char k are odd in io turull studies the case in which a is supersolvable and v is a completely reducible a module theorem 2 2 of lo extends berger s result in z the author studies a particular situation in which char k 1 1 a it is proven that if h k is a p chief factor of a solvable group g p odd and a is a p subgroup of g acting faithfully on h k then h k contains a regular a orbit the nilpotent case is open in this note we suppose that v is endowed with a g invariant nonsingular symplectic form this allows us to obtain stronger results

regular orbits of nilpotent subgroups of solvable linear groups abstract we settle a conjecture of walter carlip 1994 2 conjecture 1 3 suppose that g is a finite solvable group v is a finite faithful f g module over a field of characteristic p and assume o p g 1 let h be a nilpotent subgroup of g assume that h involves no wreath product z r z r for r 2 or r a mersenne prime then h has at least one regular orbit on v

blocks of small defect abstract let g be a finite solvable group let p be a prime such that p 5 and o p g 1 and we denote g p p n then g contains a block of defect less than or equal to 3 n 5 let g be a finite solvable group and let p a be the largest power of p dividing 1 for an irreducible character of g we show that g f g p p 3 a for p 5

on finite groups in which coprime commutators are covered by few cyclic subgroups the coprime commutators j and j were recently introduced as a tool to study properties of finite groups that can be expressed in terms of commutators of elements of coprime orders every element of a finite group g is both a 1 commutator and a 0 commutator now let j 2 and let x be the set of all elements of g that are powers of j 1 commutators an element g is a j commutator if there exist a x and b g such that g a b and a b 1 for j 1 let y be the set of all elements of g that are powers of j 1 commutators an element g is a j commutator if there exist a b y such that g a b and a b 1 the subgroups of g generated by all j commutators and all j commutators are denoted by j g and j g respectively for every j 2 the subgroup j g is precisely the last term g of the lower central series of g while for every j 1 the subgroup j g is precisely the last term of the lower central series of j 1 g that is j g j 1 g in the present paper we prove that if g possesses m cyclic subgroups whose union contains all j commutators of g then j g contains a subgroup of m bounded order which is normal in g and has the property that j g is cyclic if j 2 and g possesses m cyclic subgroups whose union contains all j commutators of g then the order of j g is m bounded

on the probability of generating a monolithic group abstract a group l is primitive monolithic if l has a unique minimal normal subgroup n and trivial frattini subgroup by p l n k we denote the conditional probability that k randomly chosen elements of l generate l given that they project onto generators for l n in this article we show that p l n k is controlled by p y s 2 where n s r and y is a 2 generated almost simple group with socle s that is contained in the normalizer in l of the first direct factor of n information about p l n k for l primitive monolithic yields various types of information about the generation of arbitrary finite and profinite groups

stochastic differential equations with reflecting boundary conditions on resout des equations differentielles stochastiques a conditions aux limites reflechissantes par une approche directe basee sur le probleme de skorokhod

fixed point free action on groups of odd order let a be a finite abelian group that acts fixed point freely on a finite solvable group g assume that g is odd and a is of squarefree exponent coprime to 6 we show that the fitting length of g is bounded by the length of the longest chain of subgroups of a

stochastic perturbation of sweeping process and a convergence result for an associated numerical scheme abstract here we present well posedness results for first order stochastic differential inclusions more precisely for sweeping process with a stochastic perturbation these results are provided in combining both deterministic sweeping process theory recently developed in edmond and thibault 2005 2006 18 19 and methods concerning the reflection of a brownian motion lions and sznitman 1984 23 and saisho 1987 31 in addition we prove convergence results for an euler scheme discretizing these stochastic differential inclusions

an asynchronous multirate decorrelator this paper examines truncated window decorrelators for an asynchronous direct sequence code division multiple access system supporting users transmitting at different bit rates we decode a user by extending the observation window over a sufficient number of its bits to characterize practical window sizes simple upper and lower bounds for the asymptotic efficiency of both the truncated window and infinite window decorrelators are developed empirical results show that as the length of the observation window increases the bounds converge rapidly to the asymptotic efficiency of the infinite window decorrelator the complexity of the receiver depends strongly on the ratio of the maximum to minimum bit rates

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

large orbits of odd order subgroups of solvable linear groups abstract suppose that g is a finite solvable group and v is a finite faithful and completely reducible g module let h be an odd order subgroup of g then h has at least two regular orbits on v v suppose in addition that v is odd then there exists v v in a regular orbit of f g h such that c h v f 2 g let g be a solvable group h be an odd order hall subgroup of g v be a faithful g module over possibly different finite fields of odd characteristic and assume that v o g is completely reducible then there exists v v such that c h v o g

good action on a finite group abstract let g and a be finite groups with a acting on g by automorphisms in this paper we introduce the concept of good action namely we say the action of a on g is good if h h b c h b for every subgroup b of a and every b invariant subgroup h of g this definition allows us to prove a new noncoprime hall higman type theorem if a is a nilpotent group acting on the finite solvable group g with c g a 1 a long standing conjecture states that h g l a where h g is the fitting height of g and l a is the number of primes dividing the order of a counted with multiplicities as an application of our result we prove the main theorem of this paper which states that the above conjecture is true if a and g have odd order the action of a on g is good and some other fairly general conditions are satisfied

frobenius groups of automorphisms with almost fixed point free kernel abstract let fh be a frobenius group with kernel f and complement h acting coprimely on the finite solvable group g by automorphisms we prove that if c g h is of fitting length n then the index of the n th fitting subgroup f n g in g is bounded in terms of c g f and f this generalizes a result of khukhro and makarenko 6 which handles the case n 1

the canonical character of metacyclic groups with a form quasiprimitive symplectic module and an application to brauer formulas of local galois groups

on groups in which engel sinks are cyclic abstract for an element g of a group g an engel sink is a subset e g such that for every x g all sufficiently long commutators x g g g belong to e g we conjecture that if g is a profinite group in which every element admits a sink that is a procyclic subgroup then g is procyclic by locally nilpotent we prove the conjecture in two cases when g is a finite group or a soluble pro p group

a non convex setup for multivalued differential equations driven by oblique subgradients abstract the paper proves the existence and uniqueness of the solution for the following multivalued deterministic variational inequality with oblique subgradients considered in a non convex domain x t h t x t x t g t x t t 0 x 0 x 0 where stands for the frechet subdifferential of the semiconvex function and the matrix application x h x is a lipschitz mapping the presence of the oblique reflection brought by the term h leads to the use of different techniques comparing to the cases of standard reflection in non convex domains or oblique reflection in convex domains the last section of the article is focused on the qualitative analysis of a non convex skorohod problem with generalized reflection and as applications stochastic variational inequalities driven by oblique frechet subgradients are addressed

regular orbits of linear groups with an application to the k gv problem 1 abstract let p be a prime g a finite group of order coprime to p and v a faithful f pg module suppose g has a normal quasi simple irreducible subgroup h we show that either g has a regular orbit on vectors or h is an alternating group and v a minimal module or h n and p are contained in a short explicit list together with the work of robinson and thompson this leads to a solution of the k gv problem for primes p 211

finite groups and lie rings with a metacyclic frobenius group of automorphisms abstract suppose that a finite group g admits a frobenius group of automorphisms fh of coprime order with cyclic kernel f and complement h such that the fixed point subgroup c g h of the complement is nilpotent of class c it is proved that g has a nilpotent characteristic subgroup of index bounded in terms of c c g f and f whose nilpotency class is bounded in terms of c and h only this generalizes the previous theorem of the authors and p shumyatsky where for the case of c g f 1 the whole group was proved to be nilpotent of c h bounded class examples show that the condition of f being cyclic is essential results based on the classification provide reduction to soluble groups then representation theory arguments are used to bound the index of the fitting subgroup lie ring methods are used for nilpotent groups a similar theorem on lie rings with a metacyclic frobenius group of automorphisms fh is also proved

sweeping by a continuous prox regular set abstract the evolution problem known as sweeping process is considered for a class of nonconvex sets called prox regular or convex assuming essentially that such sets contain in the interior a suitable subset and move continuously w r t the hausdorff distance we prove local and global existence as well as uniqueness of solutions which are continuous functions with bounded variation some examples are presented

covers and normal covers of finite groups for a finite non cyclic group g let g be the smallest integer k such that g contains k proper subgroups h1 hk with the property that every element of g is contained in h g i for some i 2 1 k and g 2 g we prove that if g is a noncyclic permutation group of degree n then g n 2 2 we then investigate the structure of the groups g with g g where g is the size of a minimal cover of g and of those with g 2

fitting height of a finite group with a frobenius group of automorphisms abstract suppose that a finite group g admits a frobenius group of automorphisms fh with kernel f and complement h such that f acts without nontrivial fixed points that is such that c g f 1 it is proved that the fitting height of g is equal to the fitting height of the fixed point subgroup c g h and the fitting series of c g h coincides with the intersections of c g h with the fitting series of g as a corollary it is also proved that for any set of primes the length of g is equal to the length of c g h

convergence en loi des suites d integrales stochastiques sur l espace mathbb d 1 de skorokhod for sequences of stochastic integrals k n x n functional limit theorems are presented these results hold under simple natural conditions

regular orbits of finite primitive solvable groups abstract suppose that a finite solvable group g acts faithfully irreducibly and quasi primitively on a finite vector space v then g has a uniquely determined normal subgroup e which is a direct product of extraspecial p groups for various p and we denote e e z e we prove that when e 5 6 7 g will have regular orbits on v this result combined with a previous result of the author will give a complete list of e such that g will have regular orbits on v

probleme de skorohod multivoque on prouve un resultat d existence et d unicite pour une generalisation par introduction d un operateur maximal monotone multivoque du probleme de skorohod avec reflexion normale deterministe associe a un convexe ferme d de r d la formulation a partir des operateurs maximaux monotones multivoques permet de considerer des drifts singuliers explosant au bord du domaine cette approche multivoque clarifie la connexion entre probleme de skorohod et semigroupes nonlineaires en guise d application on considere ensuite le cas stochastique les equations differentielles stochastiques multivoques sont ainsi revisitees par consequent cette contribution fournit une nouvelle methode de construction de diffusions reflechies normalement possedant un coefficient de derive discontinu explosif

on p groups of maximal class as groups of automorphisms abstract let p be a p group of maximal class and m be a maximal subgroup of p let be an element in p m such that c p p 2 and assume that p suppose that p acts on a finite group g in such a manner that c g m 1 we show that if c g is nilpotent then the fitting height of g is at most two and c g is contained in the fitting subgroup of g for p 2 without assuming that c g is nilpotent we prove that the fitting height h g of g is at most h c g 1 and the fitting series of c g coincides with the intersection of c g with the fitting series of g it is also proved that if c g x is of exponent dividing e for all elements x p m then the exponent of g is bounded solely in terms of e and p these results are in parallel with known results on action of frobenius and dihedral groups

cadlag skorokhod problem driven by a maximal monotone operator abstract the article deals with the existence and uniqueness of the solution of the following differential equation a cadlag skorokhod problem driven by a maximal monotone operator and with singular input generated by the cadlag function m d x t a x t d t d k t d d m t t 0 x 0 m 0 where k d is a pure jump function the jumps outside of the constrained domain d a are counteracted through the generalized projection by taking x t x t m t whenever x t m t d a approximations of the solution based on discretization and yosida penalization are also considered

fixed point free action with some regular orbits abstract let the finite group a be acting on a finite solvable group g and suppose that no non trivial element of g is fixed under the action of all the elements of a assume furthermore that a g 1 a long standing conjecture is that then the fitting height of g is bounded by the length of the longest chain of subgroups of a in 3 this was proved in the case where for every proper subgroup b of a and every b invariant elementary abelian section s of g there exists some v s such that c b v c b s we say that b has a regular orbit on s in the present paper we establish the conjecture assuming only that some of these sections have regular orbits

on the average near far resistance for mmse detection of direct sequence cdma signals with random spreading the performance of a near far resistant finite complexity minimum mean squared error mmse linear detector for demodulating direct sequence ds code division multiple access cdma signals is studied assuming that the users are assigned random signature sequences we obtain tight upper and lower bounds on the expected near far resistance of the mmse detector averaged over signature sequences and delays as a function of the processing gain and the number of users since the mmse detector is optimally near far resistant these bounds apply to any multiuser detector that uses the same observation interval and sampling rate the lower bound on near far resistance implies that even without power control linear multiuser detection provides near far resistant performance for a number of users that grows linearly with the processing gain

bv solutions of nonconvex sweeping process differential inclusion with perturbation abstract this paper is devoted to the study of differential inclusions particularly discontinuous perturbed sweeping processes in the infinite dimensional setting on the one hand the sets involved are assumed to be prox regular and to have a variation given by a function which is of bounded variation and right continuous on the other hand the perturbation satisfies a linear growth condition with respect to a fixed compact subset finally the case where the sets move in an absolutely continuous way is recovered as a consequence

near far resistance of linear receivers in chip asynchronous cdma systems with random signatures the paper quantifies the robustness of linear receivers such as minimum mean squared error and decorrelating receivers against the near far problem in chip asynchronous direct sequence code division multiple access systems with random signatures where both of those linear receivers achieve the optimum near far resistance due to the asynchronism of the system different symbols of a user see different interference structures which affect their performance differently thus instead of concentrating on any particular symbol of a user we analyze the average optimum near far resistance of a randomly selected symbol of that user by providing simple tight upper and lower bounds on it

on fixed point free automorphisms abstract let r be a cyclic group of prime order which acts on the extraspecial group f in such a way that f f r suppose rf acts on a group g so that c g f 1 and r g 1 it is proved that f c g r f g as corollaries to this it is shown that the fitting series of c g r coincides with the intersections of c g r with the fitting series of g and that when r is not a fermat prime the fitting heights of c g r and g are equal

direct products of groups and regular orbits abstract we prove the following result let p be a prime and let g be a finite p solvable group that is a direct product of two non cyclic subgroups of coprime order and let v be some faithful irreducible module for g over some field in characteristic p then g has a regular orbit that is there exists some v v such that c g v 1

primitive characters of odd order groups abstract let g be a finite group of odd order we show that if is an irreducible primitive character of g then for all primes p dividing the order of g there is a conjugacy class such that the p part of 1 divides the size of that conjugacy class we also show that for some classes of groups the entire degree of an irreducible primitive character divides the size of a conjugacy class

existence of solutions to the nonconvex sweeping process abstract in this note we prove the existence of solutions for the sweeping process problem x t nc t x t a e x t c t x 0 x0 c 0 where c is an arbitrary hausdorff lipschitzean multifunction from i 0 t onto the set of nonempty closed subsets of r d this generalizes a well known result of j j moreau 1971 in sem d analyse convexe montpelier exp 15 in the convex case

groups of automorphisms with tni centralizers abstract a subgroup h of a finite group g is called a tni subgroup if n g h h g 1 for any g g n g h let a be a group acting on g by automorphisms where c g a is a tni subgroup of g we prove that g is solvable if and only if c g a is solvable and determine some bounds for the nilpotent length of g in terms of the nilpotent length of c g a under some additional assumptions we also study the action of a frobenius group fh of automorphisms on a group g if the set of fixed points c g f of the kernel f forms a tni subgroup and obtain a bound for the nilpotent length of g in terms of the nilpotent lengths of c g f and c g h

sweeping process with regular and nonregular sets abstract differential inclusions involving the normal cone to a moving set are investigated a special attention is paid to the sweeping process associated with sets for which no regularity assumption is required

the regular module problem i in the study of induced representations the following problem arises let h ag be a finite solvable group and k a field with chark a let v be an irreducible faithful primitive k 4g module suppose h contains a normal extraspecial r subgroup r with z r z h and that a acts faith fully on r under what conditions does a have a regular direct summand in vi in this paper we consider this question under the hypotheses that g mr where 1 m is normal abelian in am a is nilpotent a mr m r 1 and r z r is a faithful irreducible am modu e we show that a has at least three regular direct summands in v unless a exp m and r satisfy certain very restrictive conditions let h ag be a finite solvable group where a is nilpotent g is normal and y4 g 1 let k be a field of characteristic not dividing a and v a zc module assume that v is faithful and irreducible the study of induced representations often leads to the following two questions 1 regular orbit problem under what conditions does a have a regular orbit on f

the fitting length of finite soluble groups ii fixed point free automorphisms abstract let g be a finite soluble group and let h g be the fitting length of g if is a fixed point free automorphism of g that is c g 1 we denote by w the composition length of a long standing conjecture is that h g w and it is known that this bound is always true if the order of g is coprime to the order of in this paper we find some bounds to h g in function of w without assuming that g 1 in particular we prove the validity of the universal bound h g 7 w 2 this improves the exponential bound known earlier from a special case of a theorem of dade

regular and p regular orbits of solvable linear groups abstract let v be a faithful g module for a finite group g and let p be a prime dividing g an orbit v g for the action of g on v is p regular if v g p g c g v p g p zhang asks the following question in zhang 1993 8 assume that a finite solvable group g acts faithfully and irreducibly on a vector space v over a finite field f if g has a p regular orbit for every prime p dividing g is it true that g will have a regular orbit on v in lu and cao 2000 4 lu and cao construct an example showing that the answer to this question is no however the example itself is not correct in this paper we study zhang s question in detail we construct examples showing that the answer to this question is no in general we also prove the following result assume a finite solvable group g of odd order acts faithfully and irreducibly on a vector space v over a field of odd characteristic if g has a p regular orbit for every prime p dividing g then g will have a regular orbit on v