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ON VERBAL SUBGROUPS IN RESIDUALLY FINITE GROUPS

Published online by Cambridge University Press:  10 June 2011

JHONE CALDEIRA
Affiliation:
Instituto de Matemática e Estatística, Universidade Federal de Goiás, Goiânia-GO, CP 131, 74001-970, Brazil (email: [email protected])
PAVEL SHUMYATSKY*
Affiliation:
Department of Mathematics, University of Brasilia, Brasilia-DF, 70910-900, Brazil (email: [email protected])
*
For correspondence; e-mail: [email protected]
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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.

Type
Research Article
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

Footnotes

Supported by Capes and CNPq-Brazil.

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