On a class of involutive Yang-Baxter groups

2025/09/08 by Meng, H., Ballester-Bolinches, A., Jiménez-Seral, P.
#16T25 #20D10 #20F16 #FOS: Mathematics #Group Theory (math.GR) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2509.06521

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~\citeCedoOkninski2025 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 \Q₈-free. We also prove that a finite soluble group with Sylow subgroups of class at most two and Sylow 2-subgroups isomorphic to Q₈ is an IYB-group.

Citations

• New classes of IYB groups
• Counterexample to a conjecture about braces
• Solubility Criteria for Hopf-Galois Structures
• Classification of braces of order p³
• On groups of I-type and involutive Yang-Baxter groups
• Involutive Yang-Baxter Groups
• Semigroups ofI-Type

Related

• Involutive Yang-Baxter Groups
• New classes of IYB groups
• On the IYB-property in some solvable groups
• Involutive Yang-Baxter groups never act as Frobenius groups
• Retractability of set theoretic solutions of the Yang-Baxter equation