Diameters of degree graphs of nonsolvable groups, II

Abstract

Let G be a finite group and let cd ( G ) be the set of irreducible character degrees of G. The degree graph Δ ( G ) is the graph whose set of vertices is the set of primes that divide degrees in cd ( G ) , with an edge between p and q if pq divides a for some degree a ∈ cd ( G ) . It is shown using the degree graphs of the finite simple groups that if G is a nonsolvable group, then the diameter of Δ ( G ) is at most 3.