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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2310.17595 |
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| _version_ | 1866909228434718720 |
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| author | d'Elbée, Christian Müller, Isabel Ramsey, Nicholas Siniora, Daoud |
| author_facet | d'Elbée, Christian Müller, Isabel Ramsey, Nicholas Siniora, Daoud |
| contents | We give a systematic study of the model theory of generic nilpotent groups and Lie algebras. We show that the Fraïssé limit of 2-nilpotent groups of exponent $p$ studied by Baudisch is 2-dependent and NSOP$_{1}$. We prove that the class of $c$-nilpotent Lie algebras over an arbitrary field, in a language with predicates for a Lazard series, is closed under free amalgamation. We show that for $2 < c$, the generic $c$-nilpotent Lie algebra over $\mathbb{F}_{p}$ is strictly NSOP$_{4}$ and $c$-dependent. Via the Lazard correspondence, we obtain the same result for $c$-nilpotent groups of exponent $p$, for an odd prime $p > c$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_17595 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Model-theoretic properties of nilpotent groups and Lie algebras d'Elbée, Christian Müller, Isabel Ramsey, Nicholas Siniora, Daoud Logic We give a systematic study of the model theory of generic nilpotent groups and Lie algebras. We show that the Fraïssé limit of 2-nilpotent groups of exponent $p$ studied by Baudisch is 2-dependent and NSOP$_{1}$. We prove that the class of $c$-nilpotent Lie algebras over an arbitrary field, in a language with predicates for a Lazard series, is closed under free amalgamation. We show that for $2 < c$, the generic $c$-nilpotent Lie algebra over $\mathbb{F}_{p}$ is strictly NSOP$_{4}$ and $c$-dependent. Via the Lazard correspondence, we obtain the same result for $c$-nilpotent groups of exponent $p$, for an odd prime $p > c$. |
| title | Model-theoretic properties of nilpotent groups and Lie algebras |
| topic | Logic |
| url | https://arxiv.org/abs/2310.17595 |