Character Degrees and Random Walks in Finite Groups of Lie Type

Character Values at Regular Elements

There has been a good deal of work in the last decade or so on computing upper bounds of irreducible character values for finite simple groups [G1, G2, GM, LS2, LP, MS-P, R]. Some of this work concerns permutation groups, some groups of Lie type. Some is aimed at worst-case behavior, some at the character values of typical or at least fairly well-behaved elements. Various applications have been...

On Finite Groups With Two Irreducible Character Degrees

Groups whose Bipartite Divisor Graph for Character Degrees Has Five Vertices

Let $G$ be a finite group and $cd^*(G)$ be the set of nonlinear irreducible character degrees of  $G$. Suppose that $rho(G)$ denotes the set of primes dividing some element of $cd^*(G)$. The bipartite divisor graph for the set of character degrees which is denoted by $B(G)$, is a bipartite graph whose vertices are the disjoint union of $rho(G)$ and $cd^*(G)$, and a vertex $p in rho(G)$ is conne...

Groups with Two Extreme Character Degrees and their Minimal Faithful Representations

for a finite group G, we denote by p(G) the minimal degree of faithful permutation representations of G, and denote by c(G), the minimal degree of faithful representation of G by quasi-permutation matrices over the complex field C. In this paper we will assume that, G is a p-group of exponent p and class 2, where p is prime and cd(G) = {1, |G : Z(G)|^1/2}. Then we will s...

AFFINE SUBGROUPS OF THE CLASSICAL GROUPS AND THEIR CHARACTER DEGREES

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 ne...