Some group-theoretical approaches to skew left braces

نویسندگان
Kurdachenko, Leonid A. ID 1
Longobardi, Patrizia ID 2
Maj, Mercede ID 3
Otal, Javier ID 4

1 Department of Algebra and Geometry School of Mathematics and Mechanics, University of Dnipro, Gagarin prospect 72, Dnipro 10, 49010 Ukraine

2 Dipartimento di Matematica, Università di Salerno, via Giovanni Paolo II, 132, 84084 Fisciano (Salerno), Italy

3 Dipartimento di Matematica, Università di Salerno, via Giovanni Paolo II, 132, 84084 Fisciano (Salerno), Italy

4 Universidad de Zaragoza, Edificio de matemáticas, C/Pedro Cerbuna 12, 50009 Zaragoza, España

doi
10.22108/ijgt.2022.132214.1776
چکیده

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.

کلیدواژه‌ها
Skew left brace, triply factorised group, Derivation, regular subgroup, nilpotency