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

 

On groups with commutators of bounded order


Author: Pavel Shumyatsky
Journal: Proc. Amer. Math. Soc. 127 (1999), 2583-2586
MSC (1991): Primary 20E26, 20F40; Secondary 20F50
Published electronically: April 9, 1999
MathSciNet review: 1616621
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Abstract: Let $p$ be a prime, $k$ a non-negative integer. We prove that if $G$ is a residually finite group such that $[x,y]^{p^k}=1$ for all $x,y\in G$, then $G'$ is locally finite.


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Additional Information

Pavel Shumyatsky
Affiliation: Department of Mathematics\ University of Brasilia\ 70910-900 Brasilia - DF, Brazil
Email: pavel@ipe.mat.unb.br

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04982-5
PII: S 0002-9939(99)04982-5
Keywords: Residually finite group, associated Lie algebra
Received by editor(s): November 15, 1997
Published electronically: April 9, 1999
Additional Notes: This work was supported by FAPDF and CNPq-Brazil
Communicated by: Ronald M. Solomon
Article copyright: © Copyright 1999 American Mathematical Society