The cohomology rings of the special affine group of Fp 2 and of PSL(3,p)

Abstract

The special affine group of Fp^2, p an odd prime, denoted Qd(p), plays an important role in the search for free actions by finite groups on products of spheres. The mod-p and integral cohomology rings of Qd(p) are computed and, as an extension of these results, the mod-p and p-primary part of the integral cohomology of the simple group PSL(3,p) are computed. Various properties of these rings are discussed.