Finite groups with K5-free prime graphs

Abstract

Let G be a finite group and let cd(G) be the set of all complex irreducible character degrees of G. Let ρ(G) be the set of primes that divide some degrees in cd(G). The prime graph Δ(G) has vertex set ρ(G) and there is an edge between two distinct vertices p and q if pq divides some character degree . In this article, we show that if Δ(G) is K5-free, then .