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On locally graded groups with a word whose values are Engel

Part of: Special aspects of infinite or finite groups

Published online by Cambridge University Press:  17 December 2015

Pavel Shumyatsky ,
Antonio Tortora  and
Maria Tota
Pavel Shumyatsky
Affiliation:
Department of Mathematics, University of Brasilia, Brasilia, Federal District 70910-900, Brazil (pavel@unb.br)
Antonio Tortora
Affiliation:
Dipartimento di Matematica, Università di Salerno, Via Giovanni Paolo II, 132-84084, Fisciano, Salerno, Italy (antortora@unisa.it; mtota@unisa.it)
Maria Tota
Affiliation:
Dipartimento di Matematica, Università di Salerno, Via Giovanni Paolo II, 132-84084, Fisciano, Salerno, Italy (antortora@unisa.it; mtota@unisa.it)
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Abstract

Let m, n be positive integers, let υ be a multilinear commutator word and let w = υm. We prove that if G is a locally graded group in which all w-values are n-Engel, then the verbal subgroup w(G) is locally nilpotent.

Keywords

Engel elementsmultilinear commutatorslocally graded groups

MSC classification

Primary: 20F45: Engel conditions
Secondary: 20F40: Associated Lie structures
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 59 , Issue 2 , May 2016 , pp. 533 - 539
Copyright
Copyright © Edinburgh Mathematical Society 2016 

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