On coleman outer automorphism groups of finite groups

Let G be a finite group and Out _Col(G) the Coleman outer automorphism group of G(for the definition, see below). The question whether Out_Col(G) is a p′-group naturally arises from the study of the normalizer problem for integral group rings, where p is a prime. In this article, some sufficient conditions for Out_Col(G) to be a p′-group are obtained. Our results generalize some well-known theorems.