Free central extensions of groups and modular Lie powers of relation modules
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- by Marianne Johnson and Ralph Stöhr PDF
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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.References
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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
- 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
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 138 (2010), 3807-3814
- MSC (2010): Primary 20E22, 20J05, 17B01
- DOI: https://doi.org/10.1090/S0002-9939-2010-10409-4
- MathSciNet review: 2679603