we present the basic results on the representation theory of the alternating groups. our approach is based on clifford theory.

For a finite group G, the character degree graph ∆(G) is the graph whose vertices are the primes dividing the degrees of the ordinary irreducible characters of G, with distinct primes p and q joined by an edge if pq divides some character degree of G. We determine all graphs with four vertices that occur as ∆(G) for some nonsolvable group G. Along with previously known results on character degr...

in this paper we describe how the degrees of the irreducible characters of the affine subgroups of the classical groups under consideration can be found inductively. in [4] gow obtained certain character degrees for all of the affine subgroups of the classical groups. we apply the method of fischer to the above groups and, in addition to the character degrees given in [4], we obtain some new ch...

by a quasi-permutation matrix we mean a square matrix over the complex field c with non-negative integral trace. thus, every permutation matrix over c is a quasipermutation matrix. for a given finite group g, let p(g) denote the minimal degree of a faithful permutation representation of g (or of a faithful representation of g by permutation matrices), let q(g) denote the minimal degree of a fai...

Let G be a finite group and χ an irreducible character of G. A simple method for constructing a representation affording χ can be used whenever G has a subgroup H such that χH has a linear constituent with multiplicity 1. In this paper we show that (with a few exceptions) if G is a simple group or a covering group of a simple group and χ is an irreducible character of G of degree between 32 and...

The aim of this paper is to show that L2(2 f ) are the only nonsolvable groups in which every irreducible character of even degree vanishes on just one conjugacy class. MSC 2000: 20C15

abstract. in this paper, we classify all of the finite p-groups with at most three non linear irreducible character kernels.