From actions of an abelian group on itself to left braces
Group Theory
2023-10-12 v2 Rings and Algebras
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.
Cite
@article{arxiv.2304.00532,
title = {From actions of an abelian group on itself to left braces},
author = {Adolfo Ballester-Bolinches and Ramón Esteban-Romero and Leonid A. Kurdachenko and Vicent Pérez-Calabuig},
journal= {arXiv preprint arXiv:2304.00532},
year = {2023}
}
Comments
20 pages. Changed title and approach with respect to previous versions. This version emphasises the role of the construction of left braces of right nilpotency class at most from an action of an abelian group on itself