3-Rewritable Nilpotent 2-Groups of Class 2 #.

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 x 1 , x 2 ,...,x n in G there exist distinct permutations s and t in S n such that x s(1) x s (2) ··· x s(n) = x t(1) x t(2) ··· x t(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. [ABSTRACT FROM AUTHOR]