On the Nilpotency of Locally Pro-p Contraction Groups
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866915250819825664 |
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| author | Beaumont, Alonso |
| author_facet | Beaumont, Alonso |
| contents | H. Glöckner and G. A. Willis have recently shown that locally pro-p contraction groups are nilpotent. The proof hinges on a fixed-point result: if the local field $\mathbb{F}_{p}(\!(t)\!)$ acts on its $d$-th power $\mathbb{F}_{p}(\!(t)\!)^{d}$ additively, continuously, and in an appropriately equivariant manner, then the action has a non-zero fixed point. We provide a short proof of this theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_15085 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Nilpotency of Locally Pro-p Contraction Groups Beaumont, Alonso Group Theory H. Glöckner and G. A. Willis have recently shown that locally pro-p contraction groups are nilpotent. The proof hinges on a fixed-point result: if the local field $\mathbb{F}_{p}(\!(t)\!)$ acts on its $d$-th power $\mathbb{F}_{p}(\!(t)\!)^{d}$ additively, continuously, and in an appropriately equivariant manner, then the action has a non-zero fixed point. We provide a short proof of this theorem. |
| title | On the Nilpotency of Locally Pro-p Contraction Groups |
| topic | Group Theory |
| url | https://arxiv.org/abs/2410.15085 |