The Essential 2-rank for Classical Groups

Abstract

Let G be a symplectic or orthogonal group defined over a finite field with odd characteristic and let D ≤ G be a Sylow 2-subgroup. In this paper, we classify the essential 2-subgroups and determine the essential 2-rank of the Frobenius category ℱ_D(G). Together with the results of An-Dietrich and Cao–An–Zeng, this completes the work of essential subgroups and essential ranks of classical groups.