3-Rewritable nilpotent 2-groups of class 2

Abstract

Let n be an integer greater than 1. A group G is said to be n-rewritable (or a Qn-group) if for every n elements x1, x 2,...,xn in G there exist distinct permutations σ and τ in Sn such that xσ(1)x σ(2)⋯xσ(n)=xτ(1)x τ(2)⋯xτ(n). In this paper, we characterize all 3-rewritable nilpotent 2-groups of class 2. Also we have found a bound for the nilpotency class of certain nilpotent 3-rewritable groups, and have shown that 3-rewritable groups satisfy a certain law. Copyright © Taylor & Francis, Inc.