On a class of involutive Yang-Baxter groups
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912589554909184 |
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| author | Meng, H. Ballester-Bolinches, A. Jiménez-Seral, P. |
| author_facet | Meng, H. Ballester-Bolinches, A. Jiménez-Seral, P. |
| contents | A group is called an involutive Yang-Baxter group (IYB-group) if it is isomorphic to the permutation group of an involutive, non-degenerate set-theoretic solution of the Yang-Baxter equation. This paper investigates finite soluble groups whose Sylow subgroups have nilpotency class at most two, addressing Cedó and Okniński's question~\cite{CedoOkninski2025} of whether such groups are IYB-groups. We establish that a finite soluble group with Sylow subgroups of class at most two is an IYB-group if its nilpotent residual is $\Q_8$-free. We also prove that a finite soluble group with Sylow subgroups of class at most two and Sylow $2$-subgroups isomorphic to $Q_8$ is an IYB-group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_06521 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On a class of involutive Yang-Baxter groups Meng, H. Ballester-Bolinches, A. Jiménez-Seral, P. Group Theory Rings and Algebras 16T25, 20D10, 20F16 A group is called an involutive Yang-Baxter group (IYB-group) if it is isomorphic to the permutation group of an involutive, non-degenerate set-theoretic solution of the Yang-Baxter equation. This paper investigates finite soluble groups whose Sylow subgroups have nilpotency class at most two, addressing Cedó and Okniński's question~\cite{CedoOkninski2025} of whether such groups are IYB-groups. We establish that a finite soluble group with Sylow subgroups of class at most two is an IYB-group if its nilpotent residual is $\Q_8$-free. We also prove that a finite soluble group with Sylow subgroups of class at most two and Sylow $2$-subgroups isomorphic to $Q_8$ is an IYB-group. |
| title | On a class of involutive Yang-Baxter groups |
| topic | Group Theory Rings and Algebras 16T25, 20D10, 20F16 |
| url | https://arxiv.org/abs/2509.06521 |