# 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

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.