The homotopy types of compact lie groups

Hans Scheerer proved that if two simply connected compact Lie groups are homotopically equivalent, then the groups are isomorphic. We give a conceptually simpler proof which shows that the result depends only on the 2 and 3 primary homotopy of the Lie groups.     

Numerical Forms

Let I be the graded ring of homogeneous rational polynomialsin n-variables which are numerical over Z. Then I is a subringof , the divided polynomial algebra over Z in the n-variables.A consequence of the main theorem is that for any positive integerk, the image of the induced homomorphism I(Z/kZ) (Z/kZ) isa finite graded ring.     

K-theory and the anti-automorphism of the Steenrod algebra

We give simple proofs of some relations in the Steenrod algebra involving the powers and their duals and show how these relations arise from -theory.