On p-parts of Brauer character degrees and p-regular conjugacy class sizes of finite groups

Abstract

Let G be a finite group, p a prime, and IBrp(G) the set of irreducible p-Brauer characters of G. Let e¯p(G) be the largest integer such that pe¯p(G) divides χ(1) for some χ∈IBrp(G). We show that |G:Op(G)|p≤pke¯p(G) for an explicitly given constant k. We also study the analogous problem for the p-parts of the conjugacy class sizes of p-regular elements of finite groups.