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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Free central extensions of groups and modular Lie powers of relation modules
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by Marianne Johnson and Ralph Stöhr PDF
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.
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