Normal subgroups and p-regular G-class sizes

Abstract

Let G be a finite p-solvable group and N be a normal subgroup of G. Suppose that the p-regular elements of N have exactly two G-conjugacy class sizes. In this paper it is shown that, if H is a p-complement of N, then either H is abelian or H is a product of a q-group for some prime q{double barred pipep and a central subgroup of G. © 2011 Elsevier Inc.