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.

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