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CONCISENESS OF COPRIME COMMUTATORS IN FINITE GROUPS

Part of: Special aspects of infinite or finite groups Representation theory of groups

Published online by Cambridge University Press:  18 July 2013

CRISTINA ACCIARRI ,
PAVEL SHUMYATSKY  and
ANITHA THILLAISUNDARAM
CRISTINA ACCIARRI*
Affiliation:
Department of Mathematics, University of Brasilia, Brasilia-DF, 70910-900, Brazil email pavel@unb.br
PAVEL SHUMYATSKY
Affiliation:
Department of Mathematics, University of Brasilia, Brasilia-DF, 70910-900, Brazil email pavel@unb.br
ANITHA THILLAISUNDARAM
Affiliation:
Institut für Algebra und Geometrie, Mathematische Fakultät, Otto-von-Guericke-Universität Magdeburg, 39016 Magdeburg, Germany email anitha.t@cantab.net
*
✉acciarricristina@yahoo.it
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Abstract

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Let $G$ be a finite group. We show that the order of the subgroup generated by coprime ${\gamma }_{k} $-commutators (respectively, ${\delta }_{k} $-commutators) is bounded in terms of the size of the set of coprime ${\gamma }_{k} $-commutators (respectively, ${\delta }_{k} $-commutators). This is in parallel with the classical theorem due to Turner-Smith that the words ${\gamma }_{k} $ and ${\delta }_{k} $ are concise.

Keywords

commutatorsconcise words

MSC classification

Secondary: 20D25: Special subgroups (Frattini, Fitting, etc.) 20F12: Commutator calculus
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 89 , Issue 2 , April 2014 , pp. 252 - 258
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc. 

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