For any integer n eq 0, 1, a group G is said to be n-abelian if it satisfies the identity (xy)^n = x^n y^n. More generally, G is called an Alperin group if it is n-abelian for some n eq 0, 1. We consider two natural ways to generalize the concept of n-abelian group: the former leads to define n-soluble and n-nilpotent groups, the latter to define n-Levi and n-Bell groups. The main goal of this paper is to present classes of generalized n-abelian groups and to point out connections among them. Besides, Section 5 contains unpublished combinatorial characterizations for Bell groups and for Alperin groups. Finally, in Section 6 we mention results of arithmetic nature.

On n-abelian groups and their generalizations

DELIZIA, Costantino;TORTORA, ANTONIO
2011-01-01

Abstract

For any integer n eq 0, 1, a group G is said to be n-abelian if it satisfies the identity (xy)^n = x^n y^n. More generally, G is called an Alperin group if it is n-abelian for some n eq 0, 1. We consider two natural ways to generalize the concept of n-abelian group: the former leads to define n-soluble and n-nilpotent groups, the latter to define n-Levi and n-Bell groups. The main goal of this paper is to present classes of generalized n-abelian groups and to point out connections among them. Besides, Section 5 contains unpublished combinatorial characterizations for Bell groups and for Alperin groups. Finally, in Section 6 we mention results of arithmetic nature.
2011
9780521279031
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11386/2701293
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
social impact