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Bulletin of the London Mathematical Society Advance Access originally published online on May 22, 2009
Bulletin of the London Mathematical Society 2009 41(5):795-803; doi:10.1112/blms/bdp041
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© 2009 London Mathematical Society

Free centre-by-nilpotent-by-abelian groups

Marianne Johnson

School of Mathematics
University of Manchester
Manchester
M13 9PL
United Kingdom
marianne.johnson@maths.manchester.ac.uk

Ralph Stöhr

School of Mathematics
University of Manchester
Manchester
M13 9PL
United Kingdom

Received 21 April 2008. Revision received 6 January 2009.

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 contain non-trivial elements of finite order.

2000 Mathematics Subject Classification 20J05, 20E22.


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