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arXiv · 2411.00669

Wilson conjecture for omega-categorical Lie algebras, the case 3-Engel characteristic 5

Christian d'Elbée
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Abstract

We prove a version of the Wilson conjecture for $ω$-categorical $3$-Engel Lie algebras over a field of characteristic $5$: every $ω$-categorical Lie algebra over $\mathbb{F}_5$ which satisfies the identity $[x,y^3] = 0$ is nilpotent. We also include an extended introduction to Wilson's conjecture: \textit{every $ω$-categorical locally nilpotent $p$-group is nilpotent}, and present variants of this conjecture and connections to local/global nilpotency problems (Burnside, Kurosh-Levitzki, Engel groups). No particular knowledge of model theory is assumed except basic notions of formulas and definable sets.

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Christian d'Elbée. 2024-11-12. Wilson conjecture for omega-categorical Lie algebras, the case 3-Engel characteristic 5. https://arxiv.org/abs/2411.00669

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