On groups of finite Prüfer rank II

Abstract

Let $G$ be a group of finite (Prüfer) rank and $\pi$ any finite set of primes. We prove, in particular, that $G$ contains a characteristic subgroup $H$ of finite index such that for every normal subgroup $Y$ of $H$ of finite index the maximal normal $\pi$-subgroup of $H/Y$ lies in the hypercentre of $H/Y$, so in particular all finite $\pi$-images of $H$ are nilpotent.