Higher homotopy associativity of power maps on finite H-spaces

Abstract

We study connected mod p finite A p -spaces admitting AC n -space structures with n < p for an odd prime p. Our result shows that if n > (p − 1)/2, then the mod p Steenrod algebra acts on the mod p cohomology of such a space in a systematic way. Moreover, we consider A p -spaces which are mod p homotopy equivalent to product spaces of odd dimensional spheres. Then we determine the largest integer n for which such a space admits an AC n -space structure compatible with the A p -space structure.