On (n+ ½)-Engel groups

Gunnar Traustason; Enrico Jabara

doi:10.1515/jgth-2019-0105

On (n+ ½)-Engel groups

Gunnar Traustason
, Enrico Jabara

Department of Mathematical Sciences

Università Ca' Foscari Venezia

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Abstract

Let n be a positive integer. We say that a group G is an (n+1/2)-Engel group if it satisfies the law [ x, y n, x ] = 1. The variety of (n+1/2)-Engel groups lies between the varieties of n-Engel groups and (n+1) -Engel groups. In this paper, we study these groups, and in particular, we prove that all (4+1/2)-Engel-groups are locally nilpotent. We also show that if G is a (4+1/2)-Engel p-group, where p ≥ 5 is a prime, then Gp is locally nilpotent.

Original language	English
Pages (from-to)	503-511
Number of pages	9
Journal	Journal of Group Theory
Volume	23
Issue number	3
Early online date	21 Dec 2019
DOIs	https://doi.org/10.1515/jgth-2019-0105
Publication status	Published - 1 May 2020

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© 2020 Walter de Gruyter GmbH, Berlin/Boston 2020.

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On (n+ ½)-Engel groups

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