Homotopy commutativity of $H$-spaces with finitely generated cohomology

Abstract

Abstract. We show that a simply connected homotopy associative and homotopy commutative mod 3 H-space with finitely generated mod 3 cohomology is homotopy equivalent to a finite product of K(Z, 2), Sp(2), the threeconnected cover Sp(2) 3 and the homotopy fiber Sp(2) 3; 3 i of the map [3 i ] : Sp(2) → K(Z, 3) for i ≥ 1. Our result also shows that a connected Cp-space in the sense of Sugawara with finitely generated mod p cohomology has the homotopy type of a finite product of K(Z, 1), K(Z, 2) and K(Z/p i , 1) for i ≥ 1.