For any integer n ≠ 0, 1, a group is said to be n-Bell if it satisfies the law [x^n, y] = [x, y^n]. In this paper we prove that every finitely generated locally graded n-Bell group embeds into the direct product of a finite n-Bell group and a torsion-free nilpotent group of class ≤2. We prove that n-Bell groups which are not locally graded always have infinite simple sections of finite exponent. Additionally, we obtain similar results for varieties of n-Levi groups and n-abelian groups defined by the laws [x^n, y] = [x, y]^n and (xy)^n = x^ny^n, respectively. We give characterizations of these groups in the locally graded case.
Locally graded Bell groups
DELIZIA, Costantino
;NICOTERA, Chiara
2007
Abstract
For any integer n ≠ 0, 1, a group is said to be n-Bell if it satisfies the law [x^n, y] = [x, y^n]. In this paper we prove that every finitely generated locally graded n-Bell group embeds into the direct product of a finite n-Bell group and a torsion-free nilpotent group of class ≤2. We prove that n-Bell groups which are not locally graded always have infinite simple sections of finite exponent. Additionally, we obtain similar results for varieties of n-Levi groups and n-abelian groups defined by the laws [x^n, y] = [x, y]^n and (xy)^n = x^ny^n, respectively. We give characterizations of these groups in the locally graded case.File in questo prodotto:
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