A CFSG-Free Explicit Jordan’s Theorem over Arbitrary Fields

Abstract

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