On (n+1/2)-Engel groups

Gunnar Traustason, Enrico Jabara

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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 languageEnglish
Pages (from-to)503-511
JournalJournal of Group Theory
Issue number3
Early online date21 Dec 2019
Publication statusPublished - 31 May 2020


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