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ON THE EXPONENT OF A VERBAL SUBGROUP IN A FINITE GROUP

Part of: Representation theory of groups

Published online by Cambridge University Press:  16 April 2013

PAVEL SHUMYATSKY
PAVEL SHUMYATSKY*
Affiliation:
Department of Mathematics, University of Brasilia, Brasilia – DF, Brazil (email: pavel@mat.unb.br)
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Abstract

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Let $w$ be a multilinear commutator word. We prove that if $e$ is a positive integer and $G$ is a finite group in which any nilpotent subgroup generated by $w$-values has exponent dividing $e$, then the exponent of the corresponding verbal subgroup $w(G)$ is bounded in terms of $e$ and $w$only.

Keywords

finite groupsverbal subgroupscommutators

MSC classification

Secondary: 20D25: Special subgroups (Frattini, Fitting, etc.)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 93 , Issue 3 , December 2012 , pp. 325 - 332
Copyright
Copyright © 2013 Australian Mathematical Publishing Association Inc. 

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