Structure of normal subgroups with three G-class sizes

Abstract

Let G be a finite group and N be a normal subgroup of G. Suppose that the set of G-conjugacy class sizes of N is {1, m, n}, with m < n and m does not divide n. In this paper, we show that N is solvable, and we determine the structure of these subgroups. © 2011 Springer-Verlag.