Ranks of the Sylow 2-subgroups of the classical groups

TL;DR

This paper determines the ranks and normal ranks of Sylow 2-subgroups in classical groups of odd characteristic, providing detailed structural insights into these algebraic objects.

Contribution

It offers the first comprehensive calculation of ranks and normal ranks for Sylow 2-subgroups in these classical groups.

Findings

Explicit ranks of Sylow 2-subgroups are established.

Normal ranks of these subgroups are characterized.

Results enhance understanding of subgroup structure in classical groups.

Abstract

We determine the ranks and normal ranks of the Sylow 2-subgroups of the classical groups of odd characteristic.