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.
Autori: | ||
Data di pubblicazione: | 2020 | |
Titolo: | On (4+1/2)-Engel groups. | |
Rivista: | JOURNAL OF GROUP THEORY | |
Digital Object Identifier (DOI): | http://dx.doi.org/10.1515/jgth-2019-0105 | |
Volume: | 23 | |
Appare nelle tipologie: | 2.1 Articolo su rivista |
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Engel-Half.pdf | Engel-Half.pdf | Documento in Pre-print | Accesso chiuso-personale | Riservato |
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