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 be a prime, a non-negative integer. We prove that if is a residually finite group such that for all , then is locally finite.

**1.**S. I. Adian,*The Burnside Problem and Identities in Groups*, Nauka, Moscow, 1975.**2.**Yu. A. Bakhturin,*Identities in Lie algebras*, Nauka, Moscow, 1985. MR**86k:17015****3.**D. Gorenstein,*Finite Groups*, Harper and Row, New York, 1968. MR**38:229****4.**B. Hartley,*Subgroups of finite index in profinite groups*, Math. Z.**168**(1979), 71-76. MR**80k:20028****5.**B. Huppert, N. Blackburn,*Finite Groups II*, Springer Verlag, Berlin, 1982. MR**84i:20001a****6.**S. V. Ivanov,*The free Burnside groups of sufficiently large exponents*, Int. J. Algebra Comput.**4**(1994), 1-308. MR**95h:20051****7.**M. Lazard,*Sur les groupes nilpotents et les anneaux de Lie*, Ann. Sci. École Norm. Supr.**71**(1954), 101-190. MR**19:529b****8.**J.S. Wilson and E. Zelmanov,*Identities for Lie algebras of pro-p groups*, J. Pure Appl. Algebra,**81**(1992), 103-109. MR**93m:17004****9.**E. Zelmanov,*The solution of the restricted Burnside problem for groups of odd exponent*, Math. USSR Izv.**36**(1991), 41-60. MR**91i:20037****10.**E. Zelmanov,*The solution of the restricted Burnside problem for 2-groups*, Math. Sb.**182**(1991), 568-592. MR**93a:20063****11.**E. Zelmanov,*Nil Rings and Periodic Groups*, The Korean Math. Soc. Lecture Notes in Math., Seoul, 1992. MR**94c:16027**

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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