Automorphism groups of nilpotent groups
\textit{M. Dugas} and \textit{R. Göbel} [Arch. Math. 54, No. 4, 340-351 (1990: Zbl 0703.20033)] proved the following result: if \(H\) is any group, there is a torsion-free nilpotent group \(G\) of class \(2\) such that \(\Aut(G)=H\ltimes\text{Stab}(G)\), where \(\text{Stab}(G)\) is the stability group of the series \(1\triangleleft Z(G)\triangleleft G\). This generalized a previous construction due to Zalesskij of a countably infinite torsion-free nilpotent group of class \(2\) with no outer automorphisms. In the present work the authors greatly extend the earlier theorem by showing that there is a full class of nilpotent groups of class \(2\) and infinite cardinality which have isomorphic automorphism groups with the same structure as in the earlier theorem.
scientific article; zbMATH DE number 1993478