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arXiv · 2410.20440

On some connections between braces and pre-Lie rings outside of the context of Lazard's correspondence

Agata Smoktunowicz
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Abstract

Let $p>3$ be a prime number and let $A$ be a brace whose additive group is a direct sum of cyclic groups of cardinalities larger than $p^{α}$ for some $α$. Suppose that either (i) $A^{\lfloor{\frac {p-1}4}\rfloor}\subseteq pA$ or that (ii) the additive group of brace $A$ has rank smaller than ${\lfloor{\frac {p-1}4}\rfloor}$. It is shown that for every natural number $i\leq α- {\frac {4α}{p-1}}$ the factor brace $A/p^{i}A$ is obtained by a formula similar to the group of flows from a left nilpotent pre-Lie ring.

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Agata Smoktunowicz. 2025-03-29. On some connections between braces and pre-Lie rings outside of the context of Lazard's correspondence. https://arxiv.org/abs/2410.20440

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