Some group-theoretical approaches to skew left braces

Abstract

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.

Keywords

• skew left brace
• triply factorised group
• derivation
• regular subgroup
• nilpotency