On left nilpotent skew braces of class 2

2025/05/11 by Ballester-Bolinches, A., Kurdachenko, L. A., Pérez-Calabuig, V. · 1 citation
#16N40 #16T25 #81R50 #FOS: Mathematics #Group Theory (math.GR) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2505.07115

Abstract

The main objective of this article is to initiate a detailed structure theory of left nilpotent skew braces B of class 2, i.e. skew braces with B³ = 0. We prove that if B is of nilpotent type, then B is centrally nilpotent. In fact, we show that B is right nilpotent of class at most 2+mr, i.e. B^(2+mr+1) = 0, where m and r are the nilpotency classes of the additive group of B and B², respectively. If B is of abelian type, then B is actually right nilpotent of class 3, i.e. B⁽⁴⁾ = 0, and this bound is best possible.

Cited by

• On finitely generated left nilpotent braces

Related

• A note on right-nil and strong-nil skew braces
• On finitely generated left nilpotent braces
• Right Nilpotency of Braces of Cardinality p⁴
• Connections between properties of the additive and the multiplicative groups of a two-sided skew brace
• From actions of an abelian group on itself to left braces