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,yn,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 {2,3}-groups are locally nilpotent. We also show that if G is a (4+1/2)-Engel p-group, where p≥5is a prime, then G^p is locally nilpotent.

On (4+1/2)-Engel groups.

Jabara, E.
Membro del Collaboration Group
;
2020

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,yn,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 {2,3}-groups are locally nilpotent. We also show that if G is a (4+1/2)-Engel p-group, where p≥5is a prime, then G^p is locally nilpotent.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10278/3725919
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