Symmetric harmoniousness of odd-order groups

Fuente: arXiv
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Main Author: Javaheri, Mohammad
Format: Preprint
Published: 2025
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author Javaheri, Mohammad
author_facet Javaheri, Mohammad
contents We prove that every odd-order group is symmetric harmonious: there exists a permutation $g_0,g_1,\ldots, g_{\ell-1}$ of elements of $G$ such that the consecutive products $g_0g_1,g_1g_2,\ldots, g_{\ell-1}g_0$ also form a permutation of elements of $G$ and $g_{\ell-i}=g_i^{-1}$ for all $1\leq i \leq \ell-1$. We apply this result to obtain new examples of R*-sequenceable groups.
format Preprint
id arxiv_https___arxiv_org_abs_2511_13430
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Symmetric harmoniousness of odd-order groups
Javaheri, Mohammad
Group Theory
05E16
We prove that every odd-order group is symmetric harmonious: there exists a permutation $g_0,g_1,\ldots, g_{\ell-1}$ of elements of $G$ such that the consecutive products $g_0g_1,g_1g_2,\ldots, g_{\ell-1}g_0$ also form a permutation of elements of $G$ and $g_{\ell-i}=g_i^{-1}$ for all $1\leq i \leq \ell-1$. We apply this result to obtain new examples of R*-sequenceable groups.
title Symmetric harmoniousness of odd-order groups
topic Group Theory
05E16
url https://arxiv.org/abs/2511.13430