Clifford theory for commutative association schemes

In this paper, Clifford's well-known theorem on irreducible characters of finite groups is generalized to finite commutative association schemes. Our theorem relates irreducible characters of finite commutative schemes to those of their strongly normal closed subsets.     

相关于Brauer图的若干例子

Brauer图对于刻画有限群的p-块是非常关键的．高零不可约（复）特征标在有限群模表示理论中的Brauer图中扮演着重要的角色．本文用若干例子阐述了关于高零不可约特征标的几个问题．     

THE ACTION OF THE LINEAR CHARACTER GROUP ON THE SET OF NON-LINEAR IRREDUCIBLE CHARACTERS THE ACTION OF THE LINEAR CHARACTER GROUP ON THE SET OF NON-LINEAR IRREDUCIBLE CHARACTERS

1. Notations and Basic ResultsLet G be a finite nonabelian group. Then frs(G/G') is an abelian group under themultiplication of characters and acts on the set of non-linear irreducible characters of G viathe multiplication of characters. The purpose of this paper is to investigate this action. Asan application of our theoryl in the end of Section 3 we give the classification of groupshaving exactly three non-linear irreducible caracters.All groups in the paper are finite. For a factor grou…     

Coset Decomposition for Semisimple Hopf Algebras

The notion of double coset for semisimple finite dimensional Hopf algebras is introduced. This is done by considering an equivalence relation on the set of irreducible characters of the dual Hopf algebra. As an application formulae for the restriction of the irreducible characters to normal Hopf subalgebras are given.     

Association Schemes with at Most Two Nonlinear Irreducible Characters and Applications to Finite Groups

An irreducible character χ of an association scheme is called nonlinear if the multiplicity of χ is greater than 1. The main result of this paper gives a characterization of commutative association schemes with at most two nonlinear irreducible characters. This yields a characterization of finite groups with at most two nonlinear irreducible characters. A class of noncommutative association schemes with at most two nonlinear irreducible character is also given.     

Two results related to the solvability of M-groups

The results of this paper are as follows: for a finite group G, if all primitive irreducible characters are linear, or if all nonmonomial irreducible characters have the same degree, then G is solvable.     

Finite 2-groups in which distinct nonlinear irreducible characters have distinct kernels

In this paper, we study finite 2-groups in which distinct nonlinear irreducible characters have distinct kernels. We prove several results concerning these groups and completely classify 2-groups with at most five nonlinear irreducible characters satisfying this property.     

Degrees of Characters and Values on Prime Order Elements

Two irreducible characters of a finite group with the same value on prime elements have the same degree.     

Clifford theory for association schemes

Clifford theory of finite groups is generalized to association schemes. It shows a relation between irreducible complex characters of a scheme and a strongly normal closed subset of the scheme. The restriction of an irreducible character of a scheme to a strongly normal closed subset contains conjugate characters with same multiplicities. Moreover some strong relations are obtained.     

Fine Control over the Projective Characters of the Centre of a Group

In this article we will study the restriction of the irreducible projective characters of a finite group to a central subgroup. We will also consider under what conditions on the restriction of such irreducible projective characters to an abelian normal subgroup that we can deduce that the subgroup is central. Finally, we will investigate the relationship between the inertia subgroup and the absolute centralizer of a central subgroup relative to a fixed 2-cocycle of the group.     

THE ACTION OF THE LINEAR CHARACTER GROUP ON THE SET OF NON-LINEAR IRREDUCIBLE CHARACTERS

Let G be a nonabelian finite group. Then Irr(G/G′) is an abelian group under the multiplication of characters and acts on the set of non-linear irreducible characters of G via the multiplication of characters. The purpose of this paper is to establish some facts about the action of linear character group on non-linear irreducible characters and determine the structures of groups G for which either all the orbit kernels are trivial or the number of orbits is at most two. Using the established results on this action, it is very easy to classify groups G having at most three nomlinear irreducible characters.     

High speed computation of group characters

This paper describes a practical procedure for computing the ordinary irreducible characters of finite groups (of orders up to 1000 or so). The novelty of the method consists of transposing the problem from the field of complex numbers into the field of integers modulop for a suitable primep. It is much easier to compute the modular characters in the latter field, and from these characters we can calculate the ordinary irreducible characters in algebraic form.     

不同不可约特征标在某一元素上取不同值的可解群

本文给出了满足下面条件的有限可解群的分类:存在某个元素,使得不同的不可约特征标在该元素 上取不同的值.     

非SM-群的一类rp~3-阶群

称有限群的不可约特征标x为SM-特征标,如果x可由某个次正规子群的线性特征标诱导得到.称有限群为SM-群,如果有限群的所有不可约特征标均为SM-特征标.通过一个例子,将说明rp~3-阶群不一定是SM-群.     

A note on degrees of irreducible π-Brauer characters

In this note, we first investigate the degrees of irreducible π-Brauer characters of a finite π-separable group G. Then we relate degrees of irreducible π-Brauer characters to class lengths of π-regular elements of G. Received: 4 April 2008     

Irreducible projective representations of finite groups

The purpose of this paper is to prove a result on the number of irreducible projective representations of a finite group with respect to a given factor set and a group of linear characters acting on them. It includes a determination of the number of classes of projectively equivalent representations as well as a result of M. Osima on the classes of linearly equivalent representations. Osima proved his result by defining and calculating on irreducible projective Brauer characters, whereas the method used here is based on Brauer's well-known result for the linear modular representations and an induction argument on suitable coverings.     

On distinct character degrees

Berkovich, Chillag and Herzog characterized all finite groups G in which all the nonlinear irreducible characters of G have distinct degrees. In this paper we extend this result showing that a similar characterization holds for all finite solvable groups G that contain a normal subgroup N, such that all the irreducible characters of G that do not contain N in their kernel have distinct degrees.     

Real Brauer characters

In this paper, we determine the structure of finite groups with a small number of real-valued irreducible Brauer characters.