The algebraic structure of skew left brace has proved to be useful as a source of settheoretic solutions of theYang-Baxter equation.We study in this paper the connections between left and rightπ-nilpotency and the st...The algebraic structure of skew left brace has proved to be useful as a source of settheoretic solutions of theYang-Baxter equation.We study in this paper the connections between left and rightπ-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.展开更多
基金supported by the research Grant PGC2018-095140-B-I00 from the Ministerio de Ciencia,Innovacion y Universidades(Spanish Government),the Agencia Estatal de Investigacion(Spain),and FEDER(European Union)PROMETEO/2017/057 from the Generalitat(Valencian Community,Spain).
文摘The algebraic structure of skew left brace has proved to be useful as a source of settheoretic solutions of theYang-Baxter equation.We study in this paper the connections between left and rightπ-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.
