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arXiv · 2211.04235

Classification of braces of cardinality $p^4$

Dora Puljić
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Abstract

We classify nilpotent pre-Lie rings of cardinality $p^4$ and thereby braces of the same cardinality, for a sufficiently large prime $p$. It has been shown that nilpotent pre-Lie rings of cardinality $p^n$ correspond to strongly nilpotent braces of the same cardinality, for sufficiently large $p$. These braces are explicitly obtained from the corresponding pre-Lie rings by the construction of the group of flows. Not right nilpotent braces of cardinality $p^4$ have been classified, hence our results finish the classification of braces of cardinality $p^4$.

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BibTeXRIS

Dora Puljić. 2022-11-08. Classification of braces of cardinality $p^4$. https://arxiv.org/abs/2211.04235

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