3-rewritable nilpotent 2-groups of class 2(#)

摘要

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(tau(n)). in G there exist distinct permutations a and tau in S-n such that x(sigma(1))x(sigma(2))...x(sigma(n)) = x(tau(1))x(tau(2))...x(tau(2)). In thispaper, 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.