From actions of an abelian group on itself to left braces

2023/04/02 by Ballester-Bolinches, Adolfo, Esteban-Romero, Ramón, Kurdachenko, Leonid A. +1 · 2 citations
#16N40 #16T25 #81R50 #FOS: Mathematics #Group Theory (math.GR) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2304.00532

Abstract

We present a construction of left braces of right nilpotency class at most two based on suitable actions of an abelian group on itself with an invariance condition. This construction allows us to recover the construction of a free right nilpotent one-generated left brace of class two.

Cited by

• On finitely generated left nilpotent braces
• Free commutative skew braces

Related

• On the structure of some one-generator nilpotent braces
• On finitely generated left nilpotent braces
• Right Nilpotency of Braces of Cardinality p⁴
• On left nilpotent skew braces of class 2
• On left braces in which every subbrace is an ideal