5-Engel Lie algebras II
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_ | 1866914973410656256 |
|---|---|
| author | Vaughan-Lee, Michael |
| author_facet | Vaughan-Lee, Michael |
| contents | In my article 5-Engel algebras published on the arXiv in 2023 I proved that 5-Engel Lie algebras of characteristic zero or prime characteristic $p>7$ are nilpotent of class at most 11. In this note I investigate the ideal ID$(x)$ generated by an element $x$ in a 5-Engel Lie algebra. In characteristic 2 and 3 this ideal does not have to be nilpotent. For all primes $p>3$ I show that Id$(x)$ is nilpotent in 5-Engel Lie algebras of characteristic $p$, and I obtain explicit (best possible) bounds on the nilpotency class. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_11524 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | 5-Engel Lie algebras II Vaughan-Lee, Michael Group Theory Rings and Algebras 17B30, 20D15, 20F45 In my article 5-Engel algebras published on the arXiv in 2023 I proved that 5-Engel Lie algebras of characteristic zero or prime characteristic $p>7$ are nilpotent of class at most 11. In this note I investigate the ideal ID$(x)$ generated by an element $x$ in a 5-Engel Lie algebra. In characteristic 2 and 3 this ideal does not have to be nilpotent. For all primes $p>3$ I show that Id$(x)$ is nilpotent in 5-Engel Lie algebras of characteristic $p$, and I obtain explicit (best possible) bounds on the nilpotency class. |
| title | 5-Engel Lie algebras II |
| topic | Group Theory Rings and Algebras 17B30, 20D15, 20F45 |
| url | https://arxiv.org/abs/2410.11524 |