image-subalgebras, Milnor basis, and cohomology of Eilenberg-MacLane spaces Original Research Article

We describe mod p cohomology rings of Eilenberg-MacLane spaces in terms of the Milnor basis rather than in terms of admissible monomials of the Steenrod algebra. We give a formula of excess for the Milnor basis elements, correcting Krainesʹ formula in odd prime case. Using the Milnor basis description, we study and characterize certain polynomial subalgebras generated by elements obtained by applying maximum number of Milnor primitives on mod p fundamental classes of Eilenberg-MacLane spaces. A simple and interesting unstable pattern emerges. These subalgebras are exact images of the BP-Thom map into mod p cohomology rings.