On 3-Rewritable Groups

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 [2] 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.

Key Words:

• Nilpotent group
• Permutable group
• Rewritable group

2000 Mathematics Subject Classification:

• 20F99
• 20D60

Notes

Communicated by M. Dixon.