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On profinite groups in which commutators are Engel

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

Published online by Cambridge University Press:  09 April 2009

Pavel Shumyatsky
Pavel Shumyatsky
Affiliation:
Department of Mathematics University of Brasilia70910—900 Brasilia DFBrazil e-mail: pavel@ipe.mat.unb.br
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Abstract

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We show that if G is a finitely generated profinite group such that [x1, x2, …, xk] is Engel for any x1, x2, …, xk ∈ G, then γ(G) is locally nilpotent, and if [x1, x2, …, xk] has finite order for any x1, x2, …, xk ∈ G then, under some additional assumptions, γk(G) is locally finite.

Keywords

profinite groupsassociated Lie algebra

MSC classification

Secondary: 20E18: Limits, profinite groups 20F40: Associated Lie structures 20F45: Engel conditions
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 70 , Issue 1 , February 2001 , pp. 1 - 9
Copyright
Copyright © Australian Mathematical Society 2001

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