Involutive Yang-Baxter groups never act as Frobenius groups

2023/12/09 by Arpan Kanrar, Kanrar, Arpan, Wolfgang Rump +1
Computer Science · Mathematics · #16T25 #81R50 #Advanced Graph Theory Research #Advanced Topics in Algebra #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.2312.06691

openalex publication_date 2023/12/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A conjecture of S. Ram'ırez states that every indecomposable non-degenerate involutive set-theoretic solution to the Yang-Baxter equation with dihedral permutation group of order 2n has cardinality 2n. The conjecture is verified for odd n and disproved for even n. The proof for odd n is obtained from the more general result that the permutation group of a finite solution never acts as a Frobenius group.

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