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

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arxiv 2403.14975 v1 pith:YFZZVKIO submitted 2024-03-22 math.QA math.GRmath.RA

classification math.QAmath.GRmath.RA
keywords nilpotentbracesmathbbcardinalityalgebrasclassificationpre-lieright
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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 $p^5$.

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