In this article the right nilpotent Fₚ-braces of cardinality p⁵ has been classified. We use the connection between nilpotent Fₚ-braces of cardinality p⁵ 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 Fₚ, we aim to provide a comprehensive classification of right nilpotent Fₚ-braces of cardinality p⁵.
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Snehashis Mukherjee (2024) studied this question.
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