Character degree sums in finite nonsolvable groups

Character Sums Associated to Finite Coxeter Groups

The main result of this paper is a character sum identity for Coxeter arrangements over finite fields which is an analogue of Macdonald’s conjecture [19] proved by Opdam [21]. 0. Introduction Throughout this paper F will denote a finite field of characteristic p different from 2. We first slightly reformulate Macdonald’s conjecture in a form which has a direct analogue over F. Let G be a finite...

Finite Abelian Groups and Character Sums

These are some notes I have written up for myself. I have compiled what I feel to be some of the most important facts concerning characters on finite abelian groups, especially from a number theoretic point of view. I decided to distribute these because I couldn’t find a single reference that covered everything that I thought was relevant to the material I will discuss on Wednesday. Of course, ...

Nonsolvable groups with few character degrees

Diameters of Degree Graphs of Nonsolvable Groups

Four-Vertex Degree Graphs of Nonsolvable Groups

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...