Triply Factorised Groups and the Structure of Skew Left Braces  

作　　者：A.Ballester-Bolinches R.Esteban-Romero 

机构地区：[1]Departament de Matematiques,Universitat de Valencia,Dr.Moliner,50,46100 Burjassot,Valencia,Spain [2]Institut Universitari de Matematica Pura i Aplicada,Universitat Politecnica de Valencia,Cami de Vera,s/n,46022 Valencia,Spain

出　　处：《Communications in Mathematics and Statistics》2022年第2期353-370,共18页数学与统计通讯（英文）

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).

摘　　要：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 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.

关 键 词：Skew left brace Trifactorised group Triply factorised group Left nilpotent skew left brace Right nilpotent skew left brace IDEAL Left Fitting ideal Factorised skew left brace 

分 类 号：O15[理学—数学]