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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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


Authors: Marianne Johnson and Ralph Stöhr
Journal: Proc. Amer. Math. Soc. 138 (2010), 3807-3814
MSC (2010): Primary 20E22, 20J05, 17B01
Published electronically: May 24, 2010
MathSciNet review: 2679603
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Abstract | References | Similar Articles | Additional Information

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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Additional Information

Marianne Johnson
Affiliation: School of Mathematics, University of Manchester, Alan Turing Building, Man- chester, M13 9PL, United Kingdom
Address at time of publication: Mathematical Institute, 24-29 St Giles’, Oxford, OX1 3LB, United Kingdom
Email: Marianne.Johnson@maths.ox.ac.uk

Ralph Stöhr
Affiliation: School of Mathematics, University of Manchester, Alan Turing Building, Man- chester, M13 9PL, United Kingdom
Email: Ralph.Stohr@manchester.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10409-4
PII: S 0002-9939(2010)10409-4
Received by editor(s): June 30, 2009
Received by editor(s) in revised form: January 27, 2010
Published electronically: May 24, 2010
Additional Notes: This research was supported by EPSRC Standard Research Grant EP/G024898/1.
Communicated by: Martin Lorenz
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.