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arXiv · 2508.07883

On finitely generated left nilpotent braces

H. Meng·A. Ballester-Bolinches·L. A. Kurdachenko·V. Pérez-Calabuig
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Abstract

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

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H. Meng, A. Ballester-Bolinches, L. A. Kurdachenko, V. Pérez-Calabuig. 2025-08-11. On finitely generated left nilpotent braces. https://arxiv.org/abs/2508.07883

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