No abstract

The aim of this paper is to classify the finite minimal non-p-supersoluble groups, p a prime number, in the p-soluble universe.

We describe the left brace structure of the structure group and the permutation group associated to an involutive, non-degenerate set-theoretic solution of the quantum Yang-Baxter equation by using the Cayley graph of its permutation group with respect to its natural generating system. We use our descriptions of the additions in both braces to obtain new properties of the structure and the permutation groups and to recover some known properties of these groups in a more transparent way.

No abstract

Skew left braces arise naturally from the study of non-degenerate set-theoretic solutions of the Yang–Baxter equation. To understand the algebraic structure of skew left braces, a study of the decomposition into minimal substructures is relevant. We introduce chief series and prove a strengthened form of the Jordan–Hölder theorem for finite skew left braces. A characterization of right nilpotency and an application to multipermutation solutions are also given.