For any integer n≠ 0, 1, a group G is said to be “n-Bell” if it satisfies the identity [xn, y]=[x, yn].
It is known that if G is an n-Bell group, then the factor group G/Z 2 (G) has finite exponent …

Abstract For any integer n= 0, 1, a group is said to be n-Bell if it satisfies the law [xn, y]=[x,
yn]. In this paper we prove that every finitely generated locally graded n-Bell group embeds …

The third author et al. in 2013, introduced and studied the concept of auto-Bell groups. A
group G is said to be n-auto-Bell if [x< sup> n, α]=[x, α< sup> n], for all x in G, α in Aut (G) and …

Let x be an element of a group G and α be an automorphism of G. Then for a positive integer
n, the autocommutator [x, n α] is defined inductively by [x, α]= x− 1xα= x− 1α (x) and [x, n+ 1 …

Given an integer n≠ 0, 1, let ℬ n be the variety of n-Bell groups defined by the law [xn, y]=[x,
yn], and let be the class of all groups G in which, for any infinite subsets X and Y of G, there …

Let n ≠ 0, 1 n≠ 0, 1 be an integer. In this paper we introduce the exterior analogues of n-
Bell, n-Levi and n-Kappe groups, and find the structural similarities between them. In …

Strongly regular relation and n-Bell groups derived from it Page 1 ITALIAN JOURNAL OF
PURE AND APPLIED MATHEMATICS – N. 49–2023 (19–28) 19 Strongly regular relation and …

In recent years, one of the most important topics in group theory, which is used in certain
groups such as n-Bell, n-Levi and n-Kappe groups, is the discussion of commutators. Let 0 …

For any integer n 0, 1, a group G is said to be n-abelian if it satisfies the identity (xy)" x" y".
More generally, G is called an Alperin group if it is n-abelian for some n 0, 1. We consider …

L'objet de ce travail est la généralisation à un groupe infini de deux résultats obtenus par
Corsi Tani et Bonafede sur la structure du groupe des endomorphismes rationnels …