On the nilpotency of locally pro-$p$ contraction groups
H. Glöckner and G. A. Willis have recently shown [2] that locally pro-$p$ contraction groups are nilpotent. The proof hinges on a fixed point result [2, Theorem B]: if the local field $\mathbb{F}_{p}(\!(t)\!)$ acts on its $d$-th power $\mathbb{F}_{p}(\!(t)\!)^{d}$ additively, continuously, and in an...
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| Format: | Article |
| Language: | English |
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Académie des sciences
2025-04-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.728/ |
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| Summary: | H. Glöckner and G. A. Willis have recently shown [2] that locally pro-$p$ contraction groups are nilpotent. The proof hinges on a fixed point result [2, Theorem B]: 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. |
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| ISSN: | 1778-3569 |