Nilpotency of skew braces and multipermutation solutions of the Yang–Baxter equation

Abstract

We study relations between different notions of nilpotency in the context of skew braces and applications to the structure of solutions to the Yang–Baxter equation. In particular, we consider annihilator nilpotent skew braces, an important class that turns out to be a brace-theoretic analog to the class of nilpotent groups. In this vein, several well-known theorems in group theory are proved in the more general setting of skew braces.