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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.08830 |
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| _version_ | 1866911310419066880 |
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| author | Javaheri, Mohammad |
| author_facet | Javaheri, Mohammad |
| contents | A group is R-harmonious if there exists a permutation $g_1,g_2,\ldots, g_{n-1}$ of the non-identity elements of $G$ such that the consecutive products $g_1g_2$, $g_2g_3$, $\ldots, g_{n-1}g_1$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_08830 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | R-harmonious groups Javaheri, Mohammad Group Theory Combinatorics A group is R-harmonious if there exists a permutation $g_1,g_2,\ldots, g_{n-1}$ of the non-identity elements of $G$ such that the consecutive products $g_1g_2$, $g_2g_3$, $\ldots, g_{n-1}g_1$ 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. |
| title | R-harmonious groups |
| topic | Group Theory Combinatorics |
| url | https://arxiv.org/abs/2512.08830 |