A CFSG-free explicit Jordan's theorem over arbitrary fields
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909909149286400 |
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| author | Bajpai, Jitendra Dona, Daniele |
| author_facet | Bajpai, Jitendra Dona, Daniele |
| contents | We prove a version of Jordan's classification theorem for finite subgroups of $\mathrm{GL}_{n}(K)$ that is at the same time quantitatively explicit, CFSG-free, and valid for arbitrary $K$. This is the first proof to satisfy all three properties at once. Our overall strategy follows Larsen and Pink [24], with explicit computations based on techniques developed by the authors and Helfgott [2, 3], particularly in relation to dimensional estimates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_11632 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A CFSG-free explicit Jordan's theorem over arbitrary fields Bajpai, Jitendra Dona, Daniele Group Theory 20G07, 20G15, 14A10 We prove a version of Jordan's classification theorem for finite subgroups of $\mathrm{GL}_{n}(K)$ that is at the same time quantitatively explicit, CFSG-free, and valid for arbitrary $K$. This is the first proof to satisfy all three properties at once. Our overall strategy follows Larsen and Pink [24], with explicit computations based on techniques developed by the authors and Helfgott [2, 3], particularly in relation to dimensional estimates. |
| title | A CFSG-free explicit Jordan's theorem over arbitrary fields |
| topic | Group Theory 20G07, 20G15, 14A10 |
| url | https://arxiv.org/abs/2411.11632 |