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On finite involutive Yang–Baxter groups


Authors: H. Meng, A. Ballester-Bolinches, R. Esteban-Romero and N. Fuster-Corral
Journal: Proc. Amer. Math. Soc. 149 (2021), 793-804
MSC (2010): Primary 81R50; Secondary 20F29, 20B35, 20F16, 20C05, 16S34, 16T25
DOI: https://doi.org/10.1090/proc/15283
Published electronically: December 17, 2020
MathSciNet review: 4198084
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Abstract | References | Similar Articles | Additional Information

Abstract: A group $G$ is said to be an involutive Yang–Baxter group, or simply an IYB-group, if it is isomorphic to the permutation group of an involutive, nondegenerate set-theoretic solution of the Yang-Baxter equation. We give new sufficient conditions for a group that can be factorised as a product of two IYB-groups to be an IYB-group. Some earlier results are direct consequences of our main theorem.


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Additional Information

H. Meng
Affiliation: Department of Mathematics, Shanghai University, Shanghai 200444, People’s Republic of China
Address at time of publication: Departament de Matemàtiques, Universitat de València, Dr. Moliner, 50, 46100 Burjassot,València, Spain
MR Author ID: 1134794
ORCID: 0000-0001-9840-5783
Email: hymeng2009@shu.edu.cn

A. Ballester-Bolinches
Affiliation: Departament de Matemàtiques, Universitat de València, Dr. Moliner, 50, 46100 Burjassot,València, Spain
Address at time of publication: Department of Mathematics, Guangdong University of Education, 510310, Guangzhou, People’s Republic of China
MR Author ID: 263725
Email: Adolfo.Ballester@uv.es

R. Esteban-Romero
Affiliation: Institut Universitari de Matemàtica Pura i Aplicada, Universitat Politècnica de València, Camí de Vera, s/n, 46022 València, Spain
Address at time of publication: Departament de Matemàtiques, Universitat de València, Dr. Moliner, 50, 46100 Burjassot,València, Spain
MR Author ID: 689040
ORCID: 0000-0002-2321-8139
Email: Ramon.Esteban@uv.es

N. Fuster-Corral
Affiliation: Departament de Matemàtiques, Universitat de València, Dr. Moliner, 50, 46100 Burjassot,València, Spain
ORCID: 0000-0003-0258-9843
Email: Neus.Fuster@uv.es

Keywords: Finite left brace, Yang–Baxter equation, involutive nondegenerate solutions, involutive Yang–Baxter group
Received by editor(s): December 1, 2019
Published electronically: December 17, 2020
Additional Notes: The research of this paper was supported by the grant PGC2018-095140-B-I00 from the Ministerio de Ciencia, Innovación y Universidades and the Agencia Estatal de Investigación, Spain, and FEDER, European Union, and by the grant PROMETEO/2017/057 from the Generalitat, Valencian Community, Spain.
The first author was supported by the predoctoral grant 201606890006 from the China Scholarship Council.
The fourth author was supported by a predoctoral grant from the “Atracció del talent” Programme from the Universitat de València.
Communicated by: Martin Liebeck
Article copyright: © Copyright 2020 American Mathematical Society