blocks with abelian defect groups of rank 2 and one simple module abstract in this paper we investigate the block that has an abelian defect group of rank 2 and its brauer correspondent has only one simple module we will get an isotypy between the block and its brauer correspondent it will generalize a result of kessar and linckelmann

on stable equivalences and blocks with one simple module using a stable equivalence due to rouquier we show that alperin s weight conjecture holds for any p block of a finite group with defect 2 whose brauer correspondent has a unique isomorphism class of simple modules

perfect generalized characters inducing the alperin mckay conjecture it is well known that the perfect isometries predicted in broue s conjecture do not always exist when the defect groups are non abelian even when the blocks have equivalent brauer categories we consider perfect generalized characters which induce bijections between the sets of irreducible characters of height zero of a block and of its brauer correspondent in the normalizer of a defect group in this way the perfect isometries predicted in broue s conjecture for blocks with abelian defect groups are generalized whilst such generalized characters do not exist in general we show that they do exist when the defect groups are non abelian trivial intersection subgroups of order p 3 as well as for 2b 2 q for q a power of two and psu 3 q for all q further we show that these blocks satisfy a generalized version of an isotypy

perfect isometries for blocks with abelian defect groups and dihedral inertial quotients of order 6 abstract let b be a p block of a finite group g with an abelian defect group p and let e be a root of b in c g p if the inertial quotient e n g p e p c g p is a dihedral group of order 6 then there is a perfect isometry from the group of generalized characters of the group algebra of the semidirect product of e and p onto the group of generalized characters of g in b

consistent third order shell theory with application to composite cylindrical cylinders a consistent third order shell theory with applications to composite circular cylinders is presented and its finite element formulation is developed the formulation has seven displacement functions and requires c 0 continuity in the displacement field the exact computation of stress resultants is carried out through numerical integration of material stiffness coefficients of the laminate a displacement finite element model is developed using lagrange elements with higher order interpolation polynomials these elements preclude any effect of shear and membranes locking comparisons of the present results with those found in the literature for typical benchmark problems involving isotropic and composite cylindrical shells are found to be excellent and show the validity of the developed shell theory and its implementation into a finite element code

a numerical solution to the gel fand levitan marchenko equation in this paper a numerical method is developed to solve the inverse scattering problem associated with two gel fand levitan marchenko integral equations this inverse problem is represented by two coupled partial differential equations the solution of these partial differential equations is two kernel functions these kernels are also related to each other through the gel fand levitan marchenko integral equations legendre gauss lobatto nodes are used to construct the n t h polynominal interpolation to approximate the solution of the kernel functions which are related to the scattering potential an example is given to demonstrate the accuracy of the proposed method

analytical and numerical solution to the two potential zakharov shabat inverse scattering problem an analytical and a numerical method are presented in order to solve the inverse scattering problem associated with the two potential zakharov shabat coupled mode equations the numerical solution which uses leapfrogging in space and time represents a direct numerical solution to the coupled gel fand levitan marchenko glm integral equations as an extension of the authors previous work on glm equations of simpler form the analytical method which is applied for one pole reflection coefficients consists in constructing appropriate differential operators which transform the coupled glm equations to ordinary linear differential equations an application of these methods for nonuniform transmission line synthesis is presented

automizers as extended reflection groups abstract let g be a finite group having an abelian sylow p subgroup p broue malle and michel have shown that if g is a simple chevalley group then the automizer of p is an irreducible complex reflection group for p not too small and different from the defining characteristic the aim in this note is to show that a suitable version of this property holds for general finite groups

geometrically nonlinear theory of multilayered plates with interlayer slips the formulation of a geometrically nonlinear theory of anisotropic multilayered plates of general layups featuring interlayer slips is discussed the theory rests on a displacement field which accounts for an arbitrary distribution of the tangential displacements through the laminate thickness fulfills a priori the static continuity conditions of tangential stresses at the layer interfaces and allows for jumps in the tangential displacements so as to provide the possibility of incorporating effects of interfacial imperfection for the interlayer displacement jump a linear shear slip law is postulated no a priori assumption is made on the type and order of the expansion in the thicknesswise direction of the tangential displacements the pertinent equations of motion and consistent boundary conditions are derived by means of the dynamic version of the principle of virtual work these are given in terms of force and moment stress resultants and in terms of generalized displacements the generalization achieved by the proposed approach is shown by deriving as particular cases the recently proposed first order and third order models for laminated plates featuring interlayer slips

on equivalences between blocks of group algebras reduction to the simple components abstract a conjecture of michel broue states that if d is an abelian sylow p subgroup of a finite group g and h n g d then the principal blocks of g and h are rickard equivalent the structure of groups with abelian sylow p subgroups as determined by p fong and m e harris raises the following question assuming that broue s conjecture holds for the simple components of g under what conditions does it hold for g itself due to the structure of g this problem requires mainly the lifting of rickard complexes to p extensions of the simple components and the construction of complexes over wreath products we give here these reduction steps which may be regarded as a clifford theory of tilting complexes

on p blocks with abelian defect groups and inertial index 2 or 3 ii abstract let g be a finite group and b be a p block of g with an abelian defect group and inertial index 2 or 3 in this paper we determine some generalized decomposition numbers of the block b

blocks with defect group z2n z2n z2m abstract in this paper we prove that a block algebra with defect group z 2 n z 2 n z 2 m where n 2 and m is arbitrary is morita equivalent to its brauer correspondent

general two dimensional theory of laminated cylindrical shells the theory accounts for a desired degree of approximation of the displacements through the thickness thus accounting for any discontinuities in their derivatives at the interface of laminae geometric nonlinearity in the sense of the von karman strains is also included navier type solutions of the linear theory are presented for simply supported boundary conditions

perfect isometries and isotypies for blocks with abelian defect groups and the inertial quotients isomorphic toz4 z2 abstract letbbe ap block of a finite groupgwith abelian defect grouppandea root ofbincg p if the inertial quotiente ng p e p cg p is isomorphic toz4 z2andp 7 then there is a perfect isometry from the group of generalized characters of some twisted group algebra of the semidirect product ofeandponto the group of generalized characters ofginb and furthermore band its brauer correspondent inng p are isotypic

deep doubly curved multilayered shell theory a two dimensional theory is presented for the analysis of deep doubly curved multilayered shells the theory is based on a kinematical approach in which the continuity conditions for displacements and shear stresses at layer interfaces and on the bounding surfaces of the shell are exactly satisfied it also takes into account refinements of the shear and membrane terms by means of trigonometric functions as proposed previously for the transverse shear the accuracy of the proposed theory is assessed through investigation of significant problems for which an exact three dimensional elasticity solution is known first the bending of a three layered laminated symmetric cross ply rectangular plate simply supported along all edges submitted to a double sinusoidal transverse loading and second the bending of a circular cylindrical panel results obtained with the model are compared with those yielded by previous theories the sensitivity of the model to edge effects for a hard clamped free edge cylindrical panel is also examined

on donovan s conjecture abstract this article contains reduction theorems for some weaker variants of donovan s conjecture which supposes that for every finite group d of prime order p there are only finitely many morita equivalence classes of p blocks of finite groups having defect groups isomorphic to d i when restricting the conjecture to the case of abelian defect groups it can be reduced to only considering p blocks of a class of groups that are close to being direct products of simple groups ii when restricting the conjecture to the case of principal blocks of finite groups having an abelian sylow p subgroup it can be reduced to only considering p blocks of simple groups a weaker version of donovan s conjecture would suppose that there are only finitely many cartan matrices of p blocks of finite groups with defect group isomorphic to a given one iii this conjecture can be reduced to only considering p blocks of quasisimple groups with centers having orders prime to p

efficient higher order shell theory for laminated composites with multiple delaminations a higher order zigzag theory has been developed for laminated composite shells with multiple delaminations general tensor based formulation is developed for arbitrary curved shell with exact geometric description a laminated shell theory with multiple delaminations for general lamination configurations is obtained by superposing a cubic varying displacement on a zigzag linearly varying displacement the von karman nonlinearity is included in the formulation for the potentialities of addressing problems requiring geometric nonlinearity such as large deflection and postbuckling problems when top and bottom surface transverse shear stress free conditions and interface transverse shear continuity conditions including delamination interfaces are imposed the displacement of the minimal degrees of freedom is obtained the proposed displacement field can systematically handle the number shape size and locations of the delaminations through the variational principle equilibrium equations and variationally consistent boundary conditions are obtained to assess the accuracy and efficiency of the present theory the linear buckling problem of cylindrical shell with multiple delaminations has been analyzed the higher order zigzag theory should work as an efficient tool for analyzing the behavior of composite laminated shells with multiple delaminations

brauer morphism between modular hecke algebras noticeable progress in the knowledge of modular representations of finite groups has been accomplished by considering papers of broue puig and scott the most general situations where one can define the relative traces ideal and the brauer morphism see 4 our aim in this paper is to describe what happens in the case of p permutation modules and certain derived modules most of our matter comes from unpublished results of l puig then to apply that to representations of split bn pairs in natural characteristic these two subjects have been treated previously in two papers the first one by scott 26 points out the possibility of setting up for permutation modules a theory analogous to brauer s for group algebra and which contains it the results he obtains are analogues of brauer s first and second main theorems and brauer s theorems on defect 0 and 1 the other paper by tinberg 29 presents the results of curtis and richen and sawada and green on irreducible modules for split v pairs in natural characteristic and certain associated indecomposable modules tinberg s paper contains two further results an induction formula leading to very precise information about the dimension of the involved modules and a computation of vertex the latter result using scott s paper our study of the link between these subjects permits us first to simplify part b several proofs of the curtis richen sawada theory existence of weights structure coefficients for the modular hecke algebra end indg k and after that to obtain certain results about indecomposable direct summands of indg k part c in particular we check that irreducible kc modules g is a split bn pair represented in natural characteristic are in l l correspondence with g conjugacy classes of pairs i rr where v is a p subgroup of g and 7c an irreducible kjlr v v module of defect 0

a numerical solution to the zakharov shabat inverse scattering problem a novel numerical method to solve the inverse scattering problem associated with the zakharov shabat coupled mode equations is developed in this problem the coupling coefficient for two propagating modes is determined from reflection data both codirectional and contradirectional coupling can be accommodated as well as the presence of bound states analytical results based on an independent analytical method are derived in order to demonstrate the accuracy of the proposed method which is applicable to a broad class of reflection data

dynamic analysis of composite plate with multiple delaminations based on higher order zigzag theory in a recent paper cho and kim journal of applied mechanics proposed a higher order cubic zigzag theory of laminated composites with multiple delaminations the proposed theory is not only accurate but also efficient because it work with a minimal number of degrees of freedom with the application of interface continuity conditions as well as bounding surface conditions of transverse shear stresses including delaminated interfaces in this work we investigate the dynamic behavior of laminated composite plates with multiple delaminations a four node finite element based on the efficient higher order zigzag plate theory of laminated composite plates with multiple delaminations is developed to refine the prediction of frequencies mode shape and time response through the dynamic version of the variational approach the dynamic equilibrium equations and variationally consistent boundary conditions are obtained natural frequency prediction and time response analysis of a composite plate with multiple delaminations demonstrate the accuracy and efficiency of the present finite element method to prevent penetration violation at the delamination interfaces unilateral contact constraints by lagrange multiplier method are applied in the time response analysis the present finite element is suitable for the prediction of dynamic response of thick composite plates with multiple and arbitrary shaped delaminations

2 blocks with minimal nonabelian defect groups abstract we study numerical invariants of 2 blocks with minimal nonabelian defect groups these groups were classified by redei see redei 1947 41 if the defect group is also metacyclic then the block invariants are known see sambale 43 in the remaining cases there are only two infinite families of interesting defect groups in all other cases the blocks are nilpotent we prove brauer s k b conjecture and olsson s conjecture for all 2 blocks with minimal nonabelian defect groups for one of the two families we also show that alperin s weight conjecture and dade s conjecture are satisfied this paper is a part of the author s phd thesis

perfect isometries for blocks with abelian defect groups and cyclic inertial quotients of order 4 abstract let b be a p block of a finite group g with an abelian defect group p and e a root of b in c g p if the inertial quotient e n g p e p c g p is a cyclic group of order 4 there is a perfect isometry from the group of generalized characters of the group algebra of the semidirect product of e and p onto the group of generalized characters of g in b

a note on olssonʼs conjecture abstract for a p block b of a finite group g with defect group d olsson conjectured that k 0 b d d where k 0 b is the number of characters in b of height 0 and d denotes the commutator subgroup of d brauer deduced olsson s conjecture in the case where d is a dihedral 2 group using the fact that certain algebraically conjugate subsections are also conjugate in g we generalize brauer s argument for arbitrary primes p and arbitrary defect groups this extends two results by robinson for p 3 we show that olsson s conjecture is satisfied for defect groups of p rank 2 and for minimal non abelian defect groups

the blocks and weights of finite special linear and unitary groups abstract this paper has two main parts first we give a classification of the l blocks of finite special linear and unitary groups sl n q in the non defining characteristic l 3 second we describe how the l weights of sl n q can be obtained from the l weights of gl n q when l gcd n q and verify the alperin weight conjecture for sl n q under the condition l gcd n q as a step to establish the alperin weight conjecture for all finite groups we prove the inductive blockwise alperin weight condition for any unipotent l block of sl n q if l gcd n q

notes on p blocks of characters of finite groups let g be a finite group and let p be a fixed prime number in this paper we shall study the numbers of irreducible characters in a p block of g with an abelian defect group and the contributions of subsections to the inner product of irreducible characters of g as is seen in 10 111 broue and puig s generalized characters which are defined in 3 are relevant for the study of p blocks with abelian defect groups they will play an important role in this paper too let k be the algebraic number field containing the gi th roots of 1 let p be a prime ideal divisor of p in k and let o be the ring of p integers in k let b be a p block and let n b be a subsection associated with b n b is a pair such that ii is a p element of g and b is a p block of c n associated with b in 3 n b is called a b g brauer element let x be an ordinary irreducible character in b the function x is the central function on g which vanishes outside the p section of rc and which is such that x x np x npe where p is a p regular element of c n and e is the block idempotent of oc n corresponding to b following i for x xi e b we denote by m xs x3 the inner product of 9 and x rnpx is equal to the inner product of 3 b and 2 by brauer and ma s orthogonality relation rnpxf is called the contribution of n b to the inner product x x by l 5b

perfect isometries and isotypies for blocks with abelian defect groups and the inertial quotients isomorphic toz3 z3 abstract letbbe ap block of a finite groupgwith abelian defect grouppandea root ofbincg p if the inertial quotiente ng p e p cg p is isomorphic toz3 z3andp 2 7 then there is a perfect isometry from the group of generalized characters of some twisted group algebra of the semidirect product ofeandponto the group of generalized characters ofginb and furthermore band its brauer correspondent inng p are isotypic

on the brauer feit bound for abelian defect groups we improve the brauer feit bound on the number of irreducible characters in a p block for abelian defect groups by making use of halasi and podoski every coprime linear group admits a base of size two http arxiv org abs 1212 0199v1 7 and kessar and malle ann math 178 2 321 384 11 we also prove brauer s k b conjecture for 2 blocks with abelian defect groups of rank at most 5 and 3 blocks and 5 blocks with abelian defect groups of rank at most 3

perfect isometries for principal blocks with abelian defect groups and elementary abelian 2 inertial quotients abstract letbbe the principalp block of a finite groupgwith an abelian defect grouppandea root ofbincg p if the inertial quotiente ng p e p cg p is an elementary abelian 2 group respectively a dihedral group of order 8 andp 3 thenband its brauer correspondent considered as blocks ofgandng p are isotypic and in particular there is a perfect isometry between them

on perfect isometries and isotypies in alternating groups perfect isometries and isotypies are constructed for alternating groups between blocks with abelian defect groups and the brauer correspondents of these blocks these perfect isometries and isotypies satisfy additional compatibility conditions which imply that an extended broue conjecture holds for the principal block of an almost simple group with an abelian sylow psubgroup and a generalized fitting subgroup isomorphic to an alternating group let g be a finite group and let 0 be a complete discrete valuation ring with field of quotients k of characteristic 0 and residue class field k of characteristic p 0 we suppose that k contains a primitive igi th root of unity in 4 6 1 michel broue posed the following isotypy conjecture let e be a block of og with abelian defect group d and let f be the brauer correspondent of e in 9ng d then e and f are isotypic blocks if g has an abelian sylow p subgroup then the conjecture can be posed for the principal block of 0g in this case the authors have shown that the conjecture holds provided an extended conjecture holds for the principal block of almost simple groups with an abelian sylow p subgroup see 10 5e in this paper the isotypy conjecture for an arbitrary block with abelian defect group is proved for alternating groups in addition the extended conjecture is proved for the principal p block of almost simple groups with abelian sylow p subgroups and generalized fitting subgroup isomorphic to an alternating group we recall the basic definitions let 0 k be the canonical quotient mapping and let og kg be the induced 0 algebra homomorphism of the group algebras in particular e e induces a bijection between central idempotents of og and kg if e is a block idempotent of og let kgemod be the category of left kge modules of finite type and let zk g e be the grothendieck group of kgemod let gv be the set of irreducible characters of g over k we identify r k g e with the free abelian group on g e v x e gv x ge x g for all g e g let cf g k be the k space of k valued class functions on g and let cf g e k be the k subspace of class functions ae in cf g k such that ao ge a g the received by the editors march 26 1996 1991 mathematics subject classification primary 20c15 20c20 secondary 20c30 the first author was supported in part by nsf grant dms 9100310 the second author was supported in part by nsa grant mda 904 92 h 3027 1997 american mathematical society

approximate solution to the gel fand levitan equation an approximate solution to the gel fand levitan equation is given for the case where g r s can be approximated by an n t h rank separable function it is necessary both to show that k r s is n t h rank of g r s and to introduce a new orthogonal set

perfect isometries for blocks with abelian defect groups and klein four inertial quotients abstract let b be a p block of a finite group g with an abelian defect group p and e a root of b in cg p if the inertial quotient e ng p e cg p is a klein four group there is a so called perfect isometry from the group of generalized characters of a suitable twisted group algebra of the semidirect product of e and p onto the group of generalized characters of g in b

cartan matrices and brauerʼs k b conjecture ii abstract this paper continues sambale 2011 28 we show that the methods developed there also work for odd primes in particular we prove brauer s k b conjecture for defect groups which contain a central cyclic subgroup of index at most 9 as a consequence the k b conjecture holds for 3 blocks of defect at most 3 in the second part of the paper we illustrate the limits of our methods by considering an example then we use the work of kessar koshitani and linckelmann 13 and thus the classification to show that the k b conjecture is satisfied for 2 blocks of defect 5 except for the extraspecial defect group d 8 d 8 as a byproduct we also obtain the block invariants of 2 blocks with minimal nonmetacyclic defect groups some proofs rely on computer computations with gap the gap group 2008 10

cartan matrices and brauer s k b conjecture abstract it is well known that the cartan matrix of a block of a finite group cannot be arranged as a direct sum of smaller matrices in this paper we address the question if this remains true for equivalent matrices the motivation for this question comes from the work of kulshammer and wada 2002 10 which contains certain bounds for the number of ordinary characters in terms of cartan invariants as an application we prove such a bound in the special case where the determinant of the cartan matrix coincides with the order of the defect group in the second part of the paper we show that brauer s k b conjecture holds for 2 blocks under some restrictions on the defect group for example the k b conjecture holds for 2 blocks if the corresponding defect group is a central extension of a metacyclic group by a cyclic group the same is true if the defect group contains a central cyclic subgroup of index 8 in particular the k b conjecture holds for 2 blocks with defect at most 4 the paper is a part of the author s phd thesis

perverse equivalences and broueʼs conjecture abstract we give a new approach to the construction of derived equivalences between blocks of finite groups based on perverse equivalences in the setting of broue s abelian defect group conjecture we provide in particular local and global perversity data describing the principal blocks and the derived equivalences for a number of finite simple groups with sylow subgroups elementary abelian of order 9 we also examine extensions to automorphism groups in a general setting

on blocks of finite groups with central hyperfocal subgroups abstract let b be a p block of a finite group g with a defect group p and a hyperfocal subgroup q p let c be a block of n g q associated with b we show that if q z p then the brauer categories of b and c are equal we show that if q is abelian and g is p solvable then b and c are morita equivalent moreover we show that if b is the principal block q is cyclic and q z p then b and c are isotypic

on the inductive blockwise alperin weight condition for classical groups abstract recently there has been substantial progress on the alperin weight conjecture as a step to establish the alperin weight conjecture for all finite groups we prove the inductive blockwise alperin weight condition for simple groups of classical type under some additional assumption

cartan invariants and central ideals of group algebras abstract in this paper we investigate general properties of cartan invariants of a finite group g in characteristic 2 one of our results shows that the cartan matrix of g in characteristic 2 contains an odd diagonal entry if and only if g contains a real element of 2 defect zero we also apply these results to 2 blocks of symmetric groups and to blocks with normal or abelian defect groups the second part of the paper deals with annihilators of certain ideals in centers of group algebras and blocks

perfect isometries and murnaghan nakayama rules acknowledgement the authors wish to thank the referee for a very careful and precise reading of several earlier versions of this manuscript they are grateful for the number quality and helpfulness of comments and suggestions received