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 x 1, x 2,…, 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). Abdollahi and Mohammadi Hassanababi in [Citation2] characterized finite groups abelian-by-cyclic in Q 3. In this article we improve their theorem, showing that the same characterization holds also for infinite abelian-by-cyclic groups and for nilpotent groups of class 2 in Q 3.
Notes
Communicated by M. Dixon.