Submission date: 26 October 2023

Abstract:

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 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.

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Full text arXiv 2310.17595: pdf, ps.