Computing skew left braces of small orders

Abstract

We improve Algorithm 5.1 of [Math. Comp. {\bf 86} (2017), 2519-2534] for computing all non-isomorphic skew left braces, and enumerate left braces and skew left braces of orders up to 868 with some exceptions. Using the enumerated data, we state some conjectures for further research.

11 pages, 8 tables, Computational results

References in corpus (5)

• Set-theoretical solutions to the quantum Yang-Baxter equation
• On set-theoretical solutions of the quantum Yang-Baxter equation
• Skew braces and the Yang-Baxter equation
• Extensions of set-theoretic solutions of the Yang-Baxter equation and a conjecture of Gateva-Ivanova
• Skew left braces of nilpotent type

Cited by in corpus (9)

• Isoclinism of skew braces
• Nilpotency in left semi-braces
• Inverse semi-braces and the Yang-Baxter equation
• Relative Rota-Baxter groups and skew left braces
• Skew braces of size $p^{2}q$ I: abelian type
• Skew braces of size $p^{2}q$ II: non-abelian type
• Enumeration of left braces with additive group $C_4\times C_4\times C_4$
• Finite skew braces with isomorphic non-abelian characteristically simple additive and circle groups
• Determining skew left braces of size np