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.
File in questo prodotto:
| File | Dimensione | Formato | |
|---|---|---|---|
|
Engel-Half.pdf
non disponibili
Descrizione: Engel-Half.pdf
Tipologia:
Documento in Pre-print
Licenza:
Accesso chiuso-personale
Dimensione
202.89 kB
Formato
Adobe PDF
|
202.89 kB | Adobe PDF | Visualizza/Apri |
I documenti in ARCA sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
