2024/02/28 by A. Ballester‐Bolinches, Ballester-Bolinches, Adolfo, R. Esteban‐Romero +7 · 2 citations
Engineering · #03D40 #16T25 #20F10 #20F16 #FOS: Mathematics #Group Theory (math.GR) #Rings and Algebras (math.RA) #Structural Analysis of Composite Materials
paper · pdf · doi:10.48550/arxiv.2402.18486
openalex publication_date 2024/02/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 non-degenerate 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.