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

2024/11/18 by Bajpai, Jitendra, Dona, Daniele · 1 citation
#14A10 #20G07 #20G15 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2411.11632

Abstract

We prove a version of Jordan's classification theorem for finite subgroups of 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.

Cited by

• Uniform expansion in finite groups of Lie type

Related

• An exposition of Jordan's original proof of his theorem on finite subgroups of \GL_n(\C)
• Modular analogues of Jordan's theorem for finite linear groups
• Product decompositions of quasirandom groups and a Jordan type theorem
• Free subgroups of special linear groups
• An arithmetic analog of Klein's classification of finite subgroups of SL₂(ℂ)