Non-simply connected H-spaces with finiteness conditions

This article is concerned with homotopy properties of H-spaces X that are reflected in the module of indecomposables QH*(X;double stroke F signp). It is shown that mod p H-spaces X of finite type with finite transcendence degree mod p cohomology and locally finite QH*(X;double stroke F signp) are Bℤ/p-null spaces, Eilenberg-MacLane spaces K(ℤ̂p, 2), K(ℤ/pr, 1), and extensions of those. If we restrict attention to H-spaces with noetherian mod p cohomology algebra, then we are left with finite mod p H-spaces and Eilenberg-MacLane spaces. © 2001 Cambridge Philosophical Society.