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On profinite groups in which commutators are Engel

Published online by Cambridge University Press:  09 April 2009

Pavel Shumyatsky
Affiliation:
Department of Mathematics University of Brasilia70910—900 Brasilia DFBrazil e-mail: [email protected]
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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, …, xkG, then γ(G) is locally nilpotent, and if [x1, x2, …, xk] has finite order for any x1, x2, …, xkG then, under some additional assumptions, γk(G) is locally finite.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2001

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