The invariants of a Sylow 2-subgroup of the finite classical groups

Abstract

The finite classical groups comprise of the general linear group, the unitary group, the symplectic group, the proper orthogonal group and the orthogonal group, over a finite field. In this thesis, we deal with five invariants of a Sylow 2-subgroup of the finite classical groups, over a field of q elements, where q is the power of some odd prime. The five invariants are as follows: the center, the number of elements of order 2 and their number of conjugacy classes, the rank and normal rank. By investigating invariants of a Sylow 2-subgroup of a given group, we can determine whether it is isomorphic to a finite classical group.