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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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Table of 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 $p > c$.