A CFSG-free explicit Jordan's theorem over arbitrary fields

Jitendra Bajpai; Daniele Dona

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arXiv · 2411.11632

A CFSG-free explicit Jordan's theorem over arbitrary fields

Jitendra Bajpai·Daniele Dona

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Abstract

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.

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Jitendra Bajpai, Daniele Dona. 2024-11-18. A CFSG-free explicit Jordan's theorem over arbitrary fields. https://arxiv.org/abs/2411.11632

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