Classification of right nilpotent ${\mathbb{F}}_p$-braces of cardinality $p^5$

Abstract

In this article the right nilpotent ${\mathbb{F}}_p$-braces of cardinality $p^5$ has been classified. We use the connection between nilpotent ${\mathbb{F}}_p$-braces of cardinality $p^5$ and nilpotent pre-Lie algebras of the same order, building on the known relationship between pre-Lie algebras and braces. Leveraging insights from the classification of nilpotent pre-Lie algebras over ${\mathbb{F}}_p$, we aim to provide a comprehensive classification of right nilpotent ${\mathbb{F}}_p$-braces of cardinality $p^5$.

28 pages. Comments are welcomed