On the Sylow Theorem for Skew Braces

2025/06/01 by A. Caranti, Caranti, A., Ilaria Del Corso +7
Engineering · #Structural Analysis and Optimization #Geotechnical Engineering and Analysis

paper · pdf · doi:10.48550/arxiv.2506.00940

Abstract

We discuss the (first) Sylow theorem for certain classes of finite skew braces, proving it to hold true when the skew brace is two-sided, bi-skew, right nilpotent, λ-homomorphic or supersoluble. We also show it to hold true for soluble skew braces that are left-nilpotent, and address a number of more specialized settings, proving general Hall-type theorems.

Citations

• On a family of simple skew braces
• Finite skew braces of square-free order and supersolubility
• Soluble skew left braces and soluble solutions of the Yang-Baxter equation
• Symmetric skew braces and brace systems
• Opposite skew left braces and applications
• Iterated matched products of finite braces and simplicity; new solutions of the Yang-Baxter equation

Related

• Sylow theory and the nilpotency class of left nilpotent skew braces
• Some properties of skew braces that are invariant under isoclinism
• A note on right-nil and strong-nil skew braces
• Finite skew braces of square-free order and supersolubility
• On left nilpotent skew braces of class 2