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Linear Groups with Almost Right Engel Elements

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

Published online by Cambridge University Press:  30 January 2019

Pavel Shumyatsky
Pavel Shumyatsky*
Affiliation:
Department of Mathematics, University of Brasilia, Brasilia-DF, 70910-900 Brazil ([email protected])
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Abstract

Let G be a linear group such that for every g ∈ G there is a finite set ${\cal R}(g)$ with the property that for every x ∈ G all sufficiently long commutators [g, x, x, …, x] belong to ${\cal R}(g)$. We prove that G is finite-by-hypercentral.

Keywords

linear groupsEngel conditionlocally nilpotent groups

MSC classification

Primary: 20E99: None of the above, but in this section
Secondary: 20F45: Engel conditions 20H20: Other matrix groups over fields
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 62 , Issue 3 , August 2019 , pp. 789 - 797
Copyright
Copyright © Edinburgh Mathematical Society 2019 

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