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ON VERBAL SUBGROUPS IN RESIDUALLY FINITE GROUPS

Part of: Special aspects of infinite or finite groups Structure and classification of infinite or finite groups

Published online by Cambridge University Press:  10 June 2011

JHONE CALDEIRA  and
PAVEL SHUMYATSKY
JHONE CALDEIRA
Affiliation:
Instituto de Matemática e Estatística, Universidade Federal de Goiás, Goiânia-GO, CP 131, 74001-970, Brazil (email: jhone@mat.ufg.br)
PAVEL SHUMYATSKY*
Affiliation:
Department of Mathematics, University of Brasilia, Brasilia-DF, 70910-900, Brazil (email: pavel@unb.br)
*
✉For correspondence; e-mail: pavel@unb.br
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Abstract

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The following theorem is proved. Let m, k and n be positive integers. There exists a number η=η(m,k,n) depending only on m, k and n such that if G is any residually finite group satisfying the condition that the product of any η commutators of the form [xm,y1,…,yk ] is of order dividing n, then the verbal subgroup of G corresponding to the word w=[xm,y1,…,yk ] is locally finite.

Keywords

residually finite groupsrestricted Burnside problemvarieties

MSC classification

Secondary: 20E10: Quasivarieties and varieties of groups 20F40: Associated Lie structures 20F50: Periodic groups; locally finite groups
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 84 , Issue 1 , August 2011 , pp. 159 - 170
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

Footnotes

Supported by Capes and CNPq-Brazil.

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