Non-solvable groups each of whose character degrees has at most two prime divisors

Abstract

In this paper, we determine all almost simple groups each of whose character degrees has at most two distinct prime divisors. More generally, we show that a finite non-solvable group [Formula: see text] with this property is an extension of an almost simple group [Formula: see text] by a solvable group and [Formula: see text], where [Formula: see text] is the set of all primes dividing some character degree of [Formula: see text].