Groups with no proper contranormal subgroups

Abstract

We consider which groups $G$ are nilpotent if they have a nilpotent normal subgroup $N$ with $G/N$ a restricted soluble group and if $G$ is the only contranormal subgroup of $G$. This supplements Kurdachenko, Otal, and Subbotin work of 2009, where they consider the corresponding question but with $G/N$ nilpotent and $N$ a restricted soluble normal subgroup.