LOOP SPACES OF H-SPACES WITH FINITELY GENERATED COHOMOLOGY

Suppose X is a simply connected mod pH-space such that the mod p cohomology H ∗ (ΩX) is a finitely generated algebra. We show that the loop space ΩX is homotopy equivalent to a finite product of Eilenberg-MacLane spaces K(Z, 1), K(Z, 2) and K(Z/p i, 1) for i ≥ 1. This is a generalization of the result due to Lin, in which the same result was proved under the assumption that X is an Ap-space. 1. Introduction. Let p be an odd prime. We assume that all spaces are completed at p in the sense of Bousfield-Kan [2], and the cohomologies are taken with Z/pcoefficients unless otherwise specified. In this paper, we investigate the homotopy type for the loop space of an H-space whose cohomology is finitel