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arXiv · 2509.06521

On a class of involutive Yang-Baxter groups

H. Meng·A. Ballester-Bolinches·P. Jiménez-Seral
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Abstract

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.

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H. Meng, A. Ballester-Bolinches, P. Jiménez-Seral. 2025-09-16. On a class of involutive Yang-Baxter groups. https://arxiv.org/abs/2509.06521

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