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Free central extensions of groups and modular Lie powers of relation modules
Author(s):
Marianne
Johnson;
Ralph
Stöhr
Journal:
Proc. Amer. Math. Soc.
138
(2010),
3807-3814.
MSC (2010):
Primary 20E22, 20J05, 17B01
Posted:
May 24, 2010
MathSciNet review:
2679603
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Abstract:
The most prominent special case of our main result is that the free centre-by-(nilpotent of class ( ))-by-abelian groups ![$ F/[\gamma_c(F'),F]$](/proc/2010-138-11/S0002-9939-2010-10409-4/gif-abstract0/img2.gif) are torsion-free whenever  is divisible by at least two distinct primes. This is in stark contrast to the case where  is a prime or  , 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:
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
Posted:
May 24, 2010
Additional Notes:
This research was supported by EPSRC Standard Research Grant EP/G024898/1.
Communicated by:
Martin Lorenz
Copyright of article:
Copyright
2010,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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