Finite skew braces of square-free order and supersolubility

Finite skew braces of square-free order and supersolubility

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The aim of this paper is to study supersoluble rubbermaid 8 gallon trash can 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 click here the Fitting ideal; also, B has finite multipermutational level if and only if $(B,+)$ is nilpotent.