Triply factorised groups and the structure of skew left braces
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Ballester-Bolinches, Adolfo; Esteban Romero, Ramón
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Aquest document és un/a article, creat/da en: 2022
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The algebraic structure of skew left brace has proved to be useful as a source of set-theoretic solutions of the Yang-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. |
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