The influence of maximal subgroups on Coleman automorphisms of finite groups

Coleman automorphisms of finite groups $G$ occur naturally in the study of the normalizer conjecture of integral group rings $\mathbb{Z}G$. The purpose of this article is to investigate the influence of maximal subgroups of $G$ on Coleman automorphisms, and then present a partial answer to a question raised by Hertweck and Kimmerle which asks whether or not $\operatorname{Out}_{\operatorname{Col}}(G)=1$ provided that $G$ has a unique minimal normal subgroup.