Model-theoretic properties of nilpotent groups and Lie algebras

Authors

Christian d'Elbée, University of Leeds
Isabel Müller, The American University in Cairo
Nicholas Ramsey, University of Notre Dame
Daoud Siniora, The American University in Cairo

Funding Number

EP/Y027833/1

Funding Sponsor

UK Research and Innovation

Second Author's Department

Mathematics & Actuarial Science Department

Fourth Author's Department

Mathematics & Actuarial Science Department

Find in your Library

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 2c.

First Page

640

Last Page

701

Comments

Article. Record derived from SCOPUS.

Recommended Citation

APA Citation

d'Elbée, C. Müller, I. Ramsey, N. & Siniora, D. (2025). Model-theoretic properties of nilpotent groups and Lie algebras. Journal of Algebra, 662, 640–701. https://doi.org/10.1016/j.jalgebra.2024.08.012

MLA Citation

d'Elbée, Christian, et al. "Model-theoretic properties of nilpotent groups and Lie algebras." Journal of Algebra, vol. 662, 2025, pp. 640–701.
https://doi.org/10.1016/j.jalgebra.2024.08.012