Higher Homotopy Commutativity of H-spaces with Finitely Generated Cohomology

Suppose X is a simply connected mod p H-space such that the mod p cohomology H∗(X;Z/p) is finitely generated as an algebra. Our first result shows that if X is an An-space, then X is the total space of a principal An-fibration with base a finite An-space and fiber a finite product of CP∞s. As an application of the first result, it is shown that if X is a quasi Cp-space, then X is homotopy equivalent to a finite product of CP∞s.