For any integer n \neq 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 \neq 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 Besides, Section 5 contains unpublished combinatorial characterizations for Bell groups and for Alperin groups.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

TORTORA, ANTONIO
2011

Abstract

For any integer n \neq 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 \neq 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 Besides, Section 5 contains unpublished combinatorial characterizations for Bell groups and for Alperin groups.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.
9780521279031
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11591/402825
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