R-harmonious groups

Mohammad Javaheri

paper

R-harmonious groups

arXiv:2512.08830

Abstract

A group is R-harmonious if there exists a permutation $g_{1}, g_{2}, \dots, g_{n - 1}$ of the non-identity elements of $G$ such that the consecutive products $g_{1} g_{2}$ , $g_{2} g_{3}$ , $\dots, g_{n - 1} g_{1}$ also form a permutation of the non-identity elements, where $n = ∣ G ∣$ . We investigate R-harmonious groups via cyclic and split extensions. Among our results, we prove that every group of odd-order not divisible by 3 is R-harmonious.