From actions of an abelian group on itself to left braces

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.

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