On Zel'manov's global nilpotence theorem for Engel Lie algebras
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866916868635230208 |
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| author | Vaughan-Lee, Michael |
| author_facet | Vaughan-Lee, Michael |
| contents | I give a proof of Zel'manov's theorem that if $L$ is an $n$-Engel Lie algebra over a field $F$ of characteristic zero then $L$ is (globally) nilpotent. This is a very important result which extends Kostrikin's theorem that $L$ is locally nilpotent if the characteristic of $F$ is zero or some prime $p>n$. Zel'manov's proof contains some striking original ideas, and I wrote this note in an effort to understand his arguments. I hope that my efforts will be of use to other mathematicians in understanding this remarkable theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_21677 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Zel'manov's global nilpotence theorem for Engel Lie algebras Vaughan-Lee, Michael Group Theory Rings and Algebras 17B30 I give a proof of Zel'manov's theorem that if $L$ is an $n$-Engel Lie algebra over a field $F$ of characteristic zero then $L$ is (globally) nilpotent. This is a very important result which extends Kostrikin's theorem that $L$ is locally nilpotent if the characteristic of $F$ is zero or some prime $p>n$. Zel'manov's proof contains some striking original ideas, and I wrote this note in an effort to understand his arguments. I hope that my efforts will be of use to other mathematicians in understanding this remarkable theorem. |
| title | On Zel'manov's global nilpotence theorem for Engel Lie algebras |
| topic | Group Theory Rings and Algebras 17B30 |
| url | https://arxiv.org/abs/2507.21677 |