On some connections between braces and pre-Lie rings outside of the context of Lazard's correspondence
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916665450561536 |
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| author | Smoktunowicz, Agata |
| author_facet | Smoktunowicz, Agata |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_20440 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On some connections between braces and pre-Lie rings outside of the context of Lazard's correspondence Smoktunowicz, Agata Group Theory 17A65, 17D99, 20F18, 20F40 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. |
| title | On some connections between braces and pre-Lie rings outside of the context of Lazard's correspondence |
| topic | Group Theory 17A65, 17D99, 20F18, 20F40 |
| url | https://arxiv.org/abs/2410.20440 |