Model-theoretic properties of nilpotent groups and Lie algebras

Funding Sponsor

UK Research and Innovation

Author's Department

Mathematics & Actuarial Science Department

Second Author's Department

Mathematics & Actuarial Science Department

Fourth Author's Department

Mathematics & Actuarial Science Department

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https://doi.org/10.1016/j.jalgebra.2024.08.012

All Authors

Christian d'Elbée Isabel Müller Nicholas Ramsey Daoud Siniora

Document Type

Research Article

Publication Title

Journal of Algebra

Publication Date

1-15-2025

doi

10.1016/j.jalgebra.2024.08.012

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 NSOP1. 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 2p is strictly NSOP4 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.

First Page

640

Last Page

701

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