The average character degree and an improvement of the It(o)over-cap-Michler theorem

The classical It (o) over cap -Michler theorem states that the degree of every ordinary irreducible character of a finite group G is coprime to a prime p if and only if the Sylow p-subgroups of G are abelian and normal. In an earlier paper [8], we used the notion of average character degree to prove an improvement of this theorem for the prime p = 2. In this follow-up paper, we obtain a full improvement for all primes. Published by Elsevier Inc.