Abstract

Throughout G will be a finite group and F will be a finite field of characteristic p > 0, although we are mainly interested in the case p ¼ 2. For convenience we assume that F is a splitting field for all subgroups of G. Let ZðpÞ denote the localization ofthe integers Z at the prime ideal pZ. If x 2 ZðpÞ, then x will denote its image modulo the unique maximal ideal of ZðpÞ. We regard x as lying in the prime field GFðpÞ of F.