Non-solvable groups and the two-prime hypothesis on conjugacy class sizes

Abstract

Abstract For a finite group G, denotes the set of non-trivial conjugacy class sizes of G. The group G is said to satisfy the two-prime hypothesis if, for every a, , the number of primes dividing the greatest common divisor of a and b is at most two. The aim of this article is to investigate the simple groups satisfying the two-prime hypothesis. Also, as a result, some non-solvable groups satisfying the two-prime hypothesis are studied.