Wilson conjecture for omega-categorical Lie algebras, the case 3-Engel characteristic 5
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910695026589696 |
|---|---|
| author | d'Elbée, Christian |
| author_facet | d'Elbée, Christian |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_00669 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Wilson conjecture for omega-categorical Lie algebras, the case 3-Engel characteristic 5 d'Elbée, Christian Logic Group Theory Rings and Algebras 03C60, 17B30, 20F18 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. |
| title | Wilson conjecture for omega-categorical Lie algebras, the case 3-Engel characteristic 5 |
| topic | Logic Group Theory Rings and Algebras 03C60, 17B30, 20F18 |
| url | https://arxiv.org/abs/2411.00669 |