Radical and weight of skew braces and their applications to structure groups of solutions of the Yang–Baxter equation

We define the radical and weight of a skew left brace provide some basic properties these notions. In particular, we obtain Wedderburn type decomposition for Artinian braces. Furthermore, prove analogues theorem Wiegold, Schur its converse in context Finally, apply results to detect torsion structure group finite bijective non-degenerate set-theoretic solution Yang–Baxter equation.