Triply Factorised Groups and the Structure of Skew Left Braces

The algebraic structure of skew left brace has proved to be useful as a source of settheoretic solutions of theYang-Baxter equation.We study in this paper the connections between left and right π-nilpotency and the structure of finite skew left braces.We also study factorisations of skew left braces and their impact on the skew left brace structure.As a consequence of our study,we define a Fitting-like ideal of a left brace.Our approach depends strongly on a description of a skew left brace in terms of a triply factorised group obtained from the action of the multiplicative group of the skew left brace on its additive group.