On {2,3,5}-groups with conjugacy classes of distinct sizes

Abstract

A finite group G is called an ah-group if any two distinct conjugacy classes of G have distinct sizes. In this paper, we show that if G is an ah-group and π(G) \subseteq {2,3,5}, where π(G) denotes the set of prime divisors of |G|, then G \cong S_3.

24 pages