On the solvability of groups with four class sizes

Felipe Román María José, ANTONIO BELTRÁN

2012

Journal of Algebra and Its Applications

It is shown that if the set of conjugacy class sizes of a finite group G is {1,m,n,mn}, where m, n are positive integers which do not divide each other, then G is up to central factors a {p,q}-group. In particular, G is solvable.