On finitely generated left nilpotent braces

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$B$ is left nilpotent of class at most 2, that is B3=0$B^3 = 0$ , then B$B$ is right nilpotent of class at most 3, that is B(4)=0$B^{(4)} = 0$ . In addition, we construct a free object in the category of finitely generated left nilpotent braces of class at most 2.