Symmetric harmoniousness of odd-order groups
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912715148099584 |
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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 |