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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| 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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| author | Beaumont, Alonso |
| author_facet | Beaumont, Alonso |
| author_sort | Beaumont, Alonso |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-d10e782a1a0a41a9aacadf29fdd379b9 |
| institution | Matheson Library |
| issn | 1778-3569 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-d10e782a1a0a41a9aacadf29fdd379b92025-08-01T07:25:08ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692025-04-01363G326727010.5802/crmath.72810.5802/crmath.728On the nilpotency of locally pro-$p$ contraction groupsBeaumont, Alonso0IRMAR, Université de Rennes, 263 Avenue du Général Leclerc, 35042 Rennes Cedex, FranceH. 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.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.728/ |
| spellingShingle | Beaumont, Alonso On the nilpotency of locally pro-$p$ contraction groups Comptes Rendus. Mathématique |
| title | On the nilpotency of locally pro-$p$ contraction groups |
| title_full | On the nilpotency of locally pro-$p$ contraction groups |
| title_fullStr | On the nilpotency of locally pro-$p$ contraction groups |
| title_full_unstemmed | On the nilpotency of locally pro-$p$ contraction groups |
| title_short | On the nilpotency of locally pro-$p$ contraction groups |
| title_sort | on the nilpotency of locally pro p contraction groups |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.728/ |
| work_keys_str_mv | AT beaumontalonso onthenilpotencyoflocallypropcontractiongroups |