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- Title
A Jordan–Hölder theorem for skew left braces and their applications to multipermutation solutions of the Yang–Baxter equation.
- Authors
Ballester-Bolinches, A.; Esteban-Romero, R.; Pérez-Calabuig, V.
- Abstract
Skew left braces arise naturally from the study of non-degenerate set-theoretic solutions of the Yang–Baxter equation. To understand the algebraic structure of skew left braces, a study of the decomposition into minimal substructures is relevant. We introduce chief series and prove a strengthened form of the Jordan–Hölder theorem for finite skew left braces. A characterization of right nilpotency and an application to multipermutation solutions are also given.
- Subjects
YANG-Baxter equation; PERMUTATIONS
- Publication
Proceedings of the Royal Society of Edinburgh: Section A: Mathematics, 2024, Vol 154, Issue 3, p793
- ISSN
0308-2105
- Publication type
Article
- DOI
10.1017/prm.2023.37