criteria for solvable radical membership via p elements abstract guralnick kunyavskii plotkin and shalev have shown that the solvable radical of a finite group g can be characterized as the set of all x g such that x y is solvable for all y g we prove two generalizations of this result firstly it is enough to check the solvability of x y for every p element y g for every odd prime p secondly if x has odd order then it is enough to check the solvability of x y for every 2 element y g

reduced fusion systems over p groups with abelian subgroup of index p ii abstract for an odd prime p we look at simple fusion systems over a finite nonabelian p group s which has an abelian subgroup a of index p when s has more than one such subgroup we reduce this to a case already studied by ruiz and viruel when a is the unique abelian subgroup of index p in s and is not essential equivalently is not radical in the fusion system we give a complete list of all possibilities which can occur this includes several families of exotic fusion systems including some which have proper strongly closed subgroups

sequential composition of twistor diagrams we regard generalized twistor diagrams as linear su p q equivariant operators on tensor products of positive ladder representations we show how a sequential composition of elementary diagrams effects the algebraic composition of the su p q equivariant operators corresponding to these elementary diagrams

some problems of wielandt revisited abstract several problems in the theory of finite permutation groups considered before by h wielandt are attacked by new and traditional methods one new method is given by the theorem that a semisimple subgroup a of a group g normalizing a different subgroup b isomorphic to a forces that the centralizer in ab of b is non trivial hence b is not the generalized fitting subgroup of its normalizer this theorem is applied in proving that the paired subconstituent g of a primitive permutation group g is faithful if the non trivial subconstituent g is regular if g is a non abelian simple group all of whose proper subgroups are solvable then the regularity of g even implies that g is faithful also several theorems are obtained for the case that a non trivial subconstituent g is nilpotent or more generally that g is subnormal in g for

a characterization of solvability for finite groups in terms of their frame abstract the frame of a group is the poset of conjugacy classes of all its proper subgroups in this paper we will prove that a finite group is solvable if and only if every collection of maximal elements of its frame has a well defined meet and the poset consisting of all such meets including the meet of the empty set is a modular lattice

controlled 2 blocks of quasisimple groups abstract controlled p blocks introduced by alperin and broue in 1979 were classified for quasisimple groups g for odd primes in 10 we classify the controlled 2 blocks of quasisimple groups g the results imply that every nilpotent 2 block of g has abelian defect groups this agrees with one of the main results proved in 15 we also give an explicit characterization of non controlled 2 blocks of all quasisimple groups this implies that the p 2 version of the block theoretic analogue of glauberman s zj theorem proved by kessar linckelmann and robinson in 27 holds for quasisimple groups g

on iterative solutions of general coupled matrix equations in this paper we study coupled matrix equations which are encountered in many systems and control applications first we extend the well known jacobi and gauss seidel iterations and present a large family of iterative methods which are then applied to develop iterative solutions to coupled sylvester matrix equations the basic idea is to regard the unknown matrices to be solved as parameters of a system to be identified and to obtain the iterative solutions by applying a hierarchical identification principle next we generalize the sylvester equations to general coupled matrix equations and propose a gradient based iterative algorithm for the solutions using a block matrix inner product the star star product we prove that the iterative algorithm always converges to the unique solutions for any initial values one advantage of the algorithms proposed is that they require less storage space in implementation than existing numerical methods finally we test the algorithms and show their effectiveness using numerical examples

criteria for the solubility and non simplicity of finite groups abstract some criteria of the non simplicity of a finite group by graph theoretical terms are derived this is then used to establish conditions under which a finite group is soluble

triangle generation of finite exceptional groups of low rank given a triple p 1 p 2 p 3 of primes the object of this paper is the study of the space hom t p1 t p2 t p3 g of homomorphisms from the triangle group t p1 t p2 t p3 to a finite simple exceptional group g of lie type b 2 2 2 g 2 g 2 or d 3 4 with a few exceptions we give precise asymptotic estimates for the size of hom t p1 t p2 t p3 g and determine the limiting probability that a randomly chosen homomorphism from t p1 t p2 t p3 to g is surjective as g infinity c 2010 elsevier inc all rights reserved

on an inequality for the hadamard product of an m matrix or an h matrix and its inverse abstract let a be an n n matrix q a min a and a denote the spectrum of a from fiedler and markham linear algebra appl 101 1988 1 song linear algebra appl 305 2000 99 and yong linear algebra appl 320 2000 167 for the hadamard products of n n m matrices and their inverses the infimum of q a a 1 is 2 n in this paper the following results are presented if q ak ak 1 tends to the infimum 2 n for n n n 2 m matrices ak k 1 2 then the spectral radius jk of the jacobi iterative matrix of ak tends to 1 that is if q a a 1 is close to 2 n then j is close to 1 and another lower bound is given for a being an n n m matrix q a a 1 max 1 j 2 1 j 1 n 2 1 n 1 j 1 n 2 where j is the spectral radius of the jacobi iterative matrix of a furthermore if a is an h matrix then q a a 1 1 jm a 2 1 jm a 2 where jm a is the spectral radius of the jacobi iterative matrix of the comparison matrix m a

rouquier blocks in chevalley groups of type e abstract in finite chevalley groups of type e we shall find a rouquier like block algebra in non defining characteristic we construct a morita equivalence between this block and a principal block of a local subgroup as an application of the equivalence we shall determine some decomposition numbers in type e

proof of a conjecture of fiedler and markham let a be an n n nonsingular m matrix for the hadamard product a a 1 m fiedler and t l markham conjectured in linear algebra appl 10l 1988 1 that q a a 1 2 n where q a a 1 is the smallest eigenvalue in modulus of a a 1 we considered this conjecture in linear algebra appl 288 1999 259 having observed an incorrect proof in linear algebra appl 144 1991 171 and obtained that q a a 1 2 n n 1 n the present paper gives a proof for this conjecture

primitive permutation groups with a solvable 2 transitive subconstituent for a permutation group g acting on a finite set and a point a suborbit is an orbit of the point stabilizer g on the permutation group induced by g on is called a subconstituent of g moreover g is said to be uniprimitive if g is primitive but not 2 transitive in this paper we investigate uniprimitive permutation groups which have a solvable 2 transitive subconstituent we determine all such groups g which have a simple socle the affine case that is g has an elementary abelian socle are also discussed and an infinite family of affine primitive groups with non self paired 2 transitive subconstituents are presented

primitive permutation groups of bounded orbital diameter we give a description of infinite families of finite primitive permutation groups for which there is a uniform finite upper bound on the diameter of all orbital graphs this is equivalent to describing families of finite permutation groups such that every ultraproduct of the family is primitive a key result is that in the almost simple case with socle of fixed lie rank apart from very specific cases there is such a diameter bound this is proved using recent results on the model theory of pseudofinite fields and difference fields

an inequality for the hadamard product of an m matrix and an inverse m matrix abstract an estimate from below the smallest eigenvalue q a c of the hadamard product a c of an m matrix a and an inverse m matrix c is proved in particular if a is an m matrix of order n we obtain the inequality q a a 1 1 n

controlled blocks of the finite quasisimple groups for odd primes abstract we classify controlled blocks introduced by alperin and broue in 1979 for all quasisimple groups g for odd primes the results imply that every nilpotent block of g has abelian defect groups which in turn is one of the main results proved in an and eaton 2011 6 we also give an explicit characterization of non controlled blocks of all quasisimple groups g for odd primes this implies the block theoretic analogue of glauberman s zj theorem for g proved by kessar linckelmann and robinson 2002 18

iterative least squares solutions of coupled sylvester matrix equations abstract in this paper we present a general family of iterative methods to solve linear equations which includes the well known jacobi and gauss seidel iterations as its special cases the methods are extended to solve coupled sylvester matrix equations in our approach we regard the unknown matrices to be solved as the system parameters to be identified and propose a least squares iterative algorithm by applying a hierarchical identification principle and by introducing the block matrix inner product the star product for short we prove that the iterative solution consistently converges to the exact solution for any initial value the algorithms proposed require less storage capacity than the existing numerical ones finally the algorithms are tested on computer and the results verify the theoretical findings

affine planes admitting a collineation group with a transitive action on the line at infinity abstract the affine planes admitting a collineation group with a transitive action on the line at infinity are investigated and an essentially complete classification is achieved when the group is almost simple a rather deep result is also obtained when the action on the line at infinity is faithful and primitive

a note on the hadamard product of matrices it is shown that the smallest eigenvalue of the hadamard product a b of two positive definite hermitian matrices is bounded from below by the smallest eigenvalue of abt

a trace inequality for m matrices and the symmetrizability of a real matrix by a positive diagonal matrix abstract the question of whether a real matrix is symmetrizable via multiplication by a diagonal matrix with positive diagonal entries is reduced to the corresponding question for m matrices and related to hadamard products in the process for a nonsingular m matrix a it is shown that tr a 1 a t n with equality if and only if a is symmetric and that the minimum eigenvalue of a 1 a is 1 with equality in the irreducible case if and only if a is positive diagonally symmetrizable

further solvable analogues of the baer suzuki theorem and generation of nonsolvable groups abstract let g be an almost simple group we prove that if x g has prime order p 5 then there exists an involution y such that x y is not solvable also if x is an involution then there exist three conjugates of x that generate a nonsolvable group unless x belongs to a short list of exceptions which are described explicitly we also prove that if x has order 6 or 9 then there exist two conjugates that generate a nonsolvable group

on a conjecture of fiedler and markham abstract for the hadamard product a a 1 of an m matrix a and its inverse a 1 fiedler and markham conjectured that q a a 1 2 n see m fiedler and t l markham linear algebra appl 101 1988 1 8 where q a a 1 is the smallest eigenvalue in modulus of a a 1 the present paper studies this conjecture an incorrect proof is given in li ching and chen ji cheng linear algebra appl 144 1991 171 178 and establishes q a a 1 2 n n 1 n for some special matrices the conjecture is proved

on an inequality for the hadamard product of an m matrix and its inverse abstract when a r n n is an m matrix we prove the following inequality q a a 1 1 for n 2 2 n for n 2 where a b is the hadamard product of two matrices a and b q b p b 1 1 and p c denotes the perron eigenvalue of a nonnegative matrix c this also gives a positive answer to the conjecture posed by fiedler and markham

unipotent elements of finite groups of lie type and realization fields of their complex representations abstract let p be a prime this paper classifies finite connected reductive groups g in characteristic p with the property that all complex character values of g belong to an unramified above p extension of the field of rational numbers the main application of these results is to the problem of describing the irreducible complex or p adic representations of g that remain absolutely irreducible under the brauer reduction modulo p an efficient approach to solve this problem for p 3 has been developed in our paper proc london math soc 3 84 2002 439 together with proc london math soc 3 84 2002 439 theorem 1 9 of the paper solves this problem for many finite connected reductive groups in characteristic p 3 additionally we show that all complex representations of any finite connected reductive group with no composition factor of type e7 2f e8 2f and e8 5f can be realized over a quadratic extension of an unramified above p extension of q