Involutive Yang-Baxter groups never act as Frobenius groups

Arpan Kanrar; Wolfgang Rump

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arXiv · 2312.06691

Involutive Yang-Baxter groups never act as Frobenius groups

Arpan Kanrar·Wolfgang Rump

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Abstract

A conjecture of S. Ram\'{\i}rez 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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BibTeX RIS

Arpan Kanrar, Wolfgang Rump. 2023-12-09. Involutive Yang-Baxter groups never act as Frobenius groups. https://arxiv.org/abs/2312.06691

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