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On groups with commutators of bounded order
Author(s):
Pavel
Shumyatsky
Journal:
Proc. Amer. Math. Soc.
127
(1999),
2583-2586.
MSC (1991):
Primary 20E26, 20F40;
Secondary 20F50
Posted:
April 9, 1999
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Abstract:
Let  be a prime,  a non-negative integer. We prove that if  is a residually finite group such that ![$[x,y]^{p^k}=1$](/proc/1999-127-09/S0002-9939-99-04982-5/gif-abstract/img5.gif) for all  , then  is locally finite.
References:
- 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:
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
Posted:
April 9, 1999
Additional Notes:
This work was supported by FAPDF and CNPq-Brazil
Communicated by:
Ronald M. Solomon
Copyright of article:
Copyright
1999,
American Mathematical Society
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