Geodesic
Finite skew braces of square-free order and supersolubility
Forum of Mathematics, Sigma, Tome 12 (2024)

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The aim of this paper is to study supersoluble skew braces, a class of skew braces that encompasses all finite skew braces of square-free order. It turns out that finite supersoluble skew braces have Sylow towers and that in an arbitrary supersoluble skew brace B many relevant skew brace-theoretical properties are easier to identify: For example, a centrally nilpotent ideal of B is B-centrally nilpotent, a fact that simplifies the computational search for the Fitting ideal; also, B has finite multipermutational level if and only if $(B,+)$ is nilpotent.Given a finite presentation of the structure skew brace $G(X,r)$ associated with a finite nondegenerate solution of the Yang–Baxter equation (YBE), there is an algorithm that decides if $G(X,r)$ is supersoluble or not. Moreover, supersoluble skew braces are examples of almost polycyclic skew braces, so they give rise to solutions of the YBE on which one can algorithmically work on. 
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A. Ballester-Bolinches; R. Esteban-Romero; M. Ferrara; V. Pérez-Calabuig; M. Trombetti. Finite skew braces of square-free order and supersolubility. Forum of Mathematics, Sigma, Tome 12 (2024). doi: 10.1017/fms.2024.29

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