Symmetric harmoniousness of odd-order groups

Mohammad Javaheri

paper

Symmetric harmoniousness of odd-order groups

arXiv:2511.13430

Abstract

We prove that every odd-order group is symmetric harmonious: there exists a permutation $g_{0}, g_{1}, \dots, g_{ℓ - 1}$ of elements of $G$ such that the consecutive products $g_{0} g_{1}, g_{1} g_{2}, \dots, g_{ℓ - 1} g_{0}$ also form a permutation of elements of $G$ and $g_{ℓ - i} = g_{i}^{- 1}$ for all $1 \leq i \leq ℓ - 1$ . We apply this result to obtain new examples of R*-sequenceable groups.