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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
DOI: https://doi.org/10.1090/S0002-9939-99-04982-5
Published electronically: April 9, 1999
MathSciNet review: 1616621
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Abstract | References | Similar Articles | Additional Information

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: https://doi.org/10.1090/S0002-9939-99-04982-5
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

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