Noetherian loop spaces

The class of loop spaces whose mod p cohomology is Noetherian is much largerthan the class of p-compact groups (for which the mod p cohomology is requiredto be finite). It contains Eilenberg-Mac Lane spaces such as the infinitecomplex projective space and 3-connected covers of compact Lie groups. We studythe cohomology of the classifying space BX of such an object and prove it is assmall as expected, that is, comparable to that of BCP^\infty. We also show thatBX differs basically from the classifying space of a p-compact group in asingle homotopy group. This applies in particular to 4-connected covers ofclassifying spaces of Lie groups and sheds new light on how the cohomology ofsuch an object looks like.