English

Abstract

Let G be a finite group and write cd(G) for the degree set of the complex irreducible characters of G. The group G is said to satisfy the two-prime hypothesis if for any distinct degrees a, b 2 cd(G), the total number of (not necessarily different) primes of the greatest common divisor gcd(a, b) is at most 2. We prove an upper bound on the number of irreducible character degrees of a nonsolvable group that has a composition factor isomorphic to PSL2(q) for q ⩾ 7.