On probabilistic identities and coset identities in pro-$p$ groups
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arXiv
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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911727617048576 |
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| author | Kionke, Steffen Otmen, Nowras Toti, Tommaso Vannacci, Matteo Weigel, Thomas |
| author_facet | Kionke, Steffen Otmen, Nowras Toti, Tommaso Vannacci, Matteo Weigel, Thomas |
| contents | It is shown that a probabilistic identity on a $σ$-compact $K$-analytic group $G$, $K$ a non-archimedean local field, is a coset identity. As an application, one concludes that compact $K$-analytic groups and various pro-$p$ groups obtained from free constructions satisfy a probabilistic Tits alternative. By means of Lie-theoretic methods, we also study torsion probabilistic identities in virtually free pro-$p$ and compact $p$-adic analytic groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_19086 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On probabilistic identities and coset identities in pro-$p$ groups Kionke, Steffen Otmen, Nowras Toti, Tommaso Vannacci, Matteo Weigel, Thomas Group Theory 20P05 (Primary) 20E18, 11M41 (Secondary) It is shown that a probabilistic identity on a $σ$-compact $K$-analytic group $G$, $K$ a non-archimedean local field, is a coset identity. As an application, one concludes that compact $K$-analytic groups and various pro-$p$ groups obtained from free constructions satisfy a probabilistic Tits alternative. By means of Lie-theoretic methods, we also study torsion probabilistic identities in virtually free pro-$p$ and compact $p$-adic analytic groups. |
| title | On probabilistic identities and coset identities in pro-$p$ groups |
| topic | Group Theory 20P05 (Primary) 20E18, 11M41 (Secondary) |
| url | https://arxiv.org/abs/2507.19086 |