On finitely generated left nilpotent braces

2025/08/11 by Meng, H., Ballester-Bolinches, A., Kurdachenko, L. A. +1
#16N40 #16T25 #81R50 #FOS: Mathematics #Group Theory (math.GR) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2508.07883

Abstract

A description of finitely generated left nilpotent braces of class at most two is presented in this paper. The description heavily depends on the fact that if B is left nilpotent of class at most 2, that is B³ = 0, then B is right nilpotent of class at most 3, that is B⁽⁴⁾ = 0. In addition, we construct a free object in the category of finitely generated left nilpotent braces of class at most 2.

Citations

• On left nilpotent skew braces of class 2
• On the structure of some one-generator nilpotent braces
• From actions of an abelian group on itself to left braces
• On the Structure of Some One-generator Braces
• Central nilpotency of skew braces
• On Engel groups, nilpotent groups, rings, braces and the Yang-Baxter equation

Related

• On left nilpotent skew braces of class 2
• On the structure of some one-generator nilpotent braces
• From actions of an abelian group on itself to left braces
• Right Nilpotency of Braces of Cardinality p⁴
• A note on right-nil and strong-nil skew braces