University of Isfahan International Journal of Group Theory 2251-7650 12 2 2023 06 01 Some group-theoretical approaches to skew left braces 99 109 26447 10.22108/ijgt.2022.132214.1776 EN Adolfo Ballester Bolinches Departament de Matemàtiques, Universitat de València, Dr. Moliner, 50, Burjassot, València, Spain Ramon Esteban-Romero Departament de Matemàtiques, Universitat de València, Dr. Moliner, 50, Burjassot, València, Spain Paz Jiménez-Seral Departamento de Matemáticas, Universidad de Zaragoza, Pedro Cerbuna, 12, Zaragoza, Spain Vicent Pérez-Calabuig Departament de Matemàtiques, Universitat de València, Dr. Moliner, 50, Burjassot, València, Spain Journal Article 2022 01 07 The algebraic structure of skew left brace has become a useful tool to construct set-theoretic solutions of the Yang-Baxter equation. In this survey we present some descriptions of skew left braces in terms of bijective derivations, triply factorised groups, and regular subgroups of the holomorph of a group, as well as some applications of these descriptions to the study of substructures, nilpotency, and factorised skew left braces.

https://ijgt.ui.ac.ir/article_26447_d4e21911b3496123e5ec512f5186c689.pdf