Coleman automorphisms of holomorphs of finite abelian groups. (Q741235)

Let \(G\) be a finite group, \(\mathbb ZG\) its integral group ring. The authors, in a series of papers, a recent one is [J. Algebra Appl. 13, No. 5, Article ID 1350156 (2014; Zbl 1303.16038)], consider the normalizer problem, that is, whether in \(U\mathbb ZG)\) the normalizer \(N_{U(\mathbb ZG)}(G)\) is \(GZ(U(\mathbb ZG))\), and also the group \(\text{Out}_C(G)\) of outer Coleman automorphisms of \(G\), because triviality of \(\text{Out}_C(G)\) implies the normalizer property for \(G\). The main result of the paper is that if \(H\) is the holomorph of a finite abelian group then \(\text{Out}_C(H)\) is trivial.