CONWAY GROUP CO3 AND THE DICKSON INVARIANTS

In this paper, we construct a map from the classifying space BC(o3) of Conway's sporadic simple group C(o3) to the classifying space BDI(4) of the new finite loop space at the prime two DI(4) of Dwyer and Wilkerson. This map has the property that it injects the mod two cohomology of BDI(4) (which is equal to the Dickson invariants of rank four) as a sub-ring over which the mod two cohomology of BC(o3) is finitely generated as a module.