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arXiv · 2202.00085

On the passage from finite braces to pre-Lie rings

Agata Smoktunowicz
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Abstract

Let p be a prime number. We show that there is a one-to-one correspondence between the set of strongly nilpotent braces and the set of nilpotent pre-Lie rings of cardinality $p^{n}$, for sufficiently large p. Moreover, there is an injective mapping from the set of left nilpotent pre-Lie rings into the set of left nilpotent braces of cardinality $p^{n}$ for n+1<p. For the passage from pre-Lie rings to braces we use exactly the same method as suggested in [41].

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Agata Smoktunowicz. 2022-01-31. On the passage from finite braces to pre-Lie rings. https://arxiv.org/abs/2202.00085

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