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 Q_n-group) if for every n elements x₁, x₂,…,x_n in G there exist distinct permutations σ and τ in S_n such that x_σ(1)x_{σ (2)} ??? x_σ(n) = x_τ(1)x_τ(2) ??? x_τ(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.