Classification of right nilpotent Fp-braces of cardinality p5

Abstract

In this article the right nilpotent $F_p$-braces of cardinality $p^5$ has been classified. We use the connection between nilpotent $F_p$-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 $F_p$, we aim to provide a comprehensive classification of right nilpotent $F_p$-braces of cardinality $p^5$.