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 $ G $ be a group‎,‎ we say that $ G $ satisfies the property $\mathcal {T}(\infty) $ provided
that‎,‎ every infinite set of elements of $ G $ contains elements $ x\neq y‎,‎ z $ such that $[x‎,‎ y‎,‎ …

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 …

Let 𝐺 be a group. For 𝑥, 𝑦∈ 𝐺, we denote [𝑥, 𝑦]= xyx− 1y− 1 and 𝑥= 𝑦𝑥𝑦− 1 𝑦. Also let 𝐺⨂
𝐺 be the group generated by the symbols 𝑥⨂ 𝑦 with the following properties 𝑥⨂ 𝑦𝑧=(𝑥⨂ …

A note on groups with a modularity condition on infinite subsets | SpringerLink Skip to main
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Abstract Let Bn and An be the varieties of groups defined by the laws (xy) n (yx)− n= 1 and
xny (yxn)− 1= 1, respectively. Let B∗ n and (An)∗ be the classes of groups in which for any …

ON n-KAPPE GROUPS Communicated by Patrizia Longobardi 1. Introduction Let w be a word
in a free group of rank n > 0. Let V = Page 1 www.theoryofgroups.ir International Journal of …

ENGEL CONDITIONS ON ORDERABLE GROUPS AND IN COMBINATORIAL PROBLEMS (A
SURVEY) Abstract 1 Introduction. Page 1 ENGEL CONDITIONS ON ORDERABLE GROUPS AND …