Free central extensions of groups and modular Lie powers of relation modules

Johnson, Marianne; Stöhr, Ralph

doi:10.1090/S0002-9939-2010-10409-4

Free central extensions of groups and modular Lie powers of relation modules
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Proc. Amer. Math. Soc. 138 (2010), 3807-3814 Request permission

Abstract:

The most prominent special case of our main result is that the free centre-by-(nilpotent of class ($c-1$))-by-abelian groups $F/[\gamma _c(F’),F]$ are torsion-free whenever $c$ is divisible by at least two distinct primes. This is in stark contrast to the case where $c$ is a prime or $c=4$, where these relatively free groups contain non-trivial elements of finite order.

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