# Free centre-by-nilpotent-by-abelian groups

Johnson, Marianne and Stöhr, Ralph (2009) Free centre-by-nilpotent-by-abelian groups. Bulletin of the London Mathematical Society, 41 (5). pp. 795-803. ISSN 0024-6093

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## Abstract

We prove that the free centre-by-(nilpotent-of-class-$(c-1)$)-by-abelian groups $F/[\gamma_c(F'),F]$ are torsion-free for $c=6$. This is in startling contrast to the cases when $c$ is a prime and when $c=4$, where these relatively free groups do contain non-trivial elements of finite order.

Item Type: Article free central extensions, torsion, homology, modular Lie powers MSC 2010, the AMS's Mathematics Subject Classification > 20 Group theory and generalizations Prof Ralph Stöhr 28 Oct 2009 20 Oct 2017 14:12 http://eprints.maths.manchester.ac.uk/id/eprint/1345

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