Remarks on the length of conjugacy classes of finite groups

Abstract

Let G be a finite group. The question of how certain arithmetical conditions on the lengths of the conjugacy classes of G influence the group structure has been studied by several authors. In this paper we study restrictions on the structure of a finite group in which the lengths of conjugacy classes are not divisible by p 2 for some prime p. We generalise and provide simplified proofs for some earlier results.