Ran Levi Northwestern University (previous, University of Heidelberg) A comparison Criterion for certain loop spaces We study a comparison criterion for loop spaces on $p$-localized classifying spaces of certain finite $p$-perfect groups $G$. In particular we show that, under certain hypotheses, the homotopy type of those spaces is determined by the mod-$p$ cohomology of $G$ together with a finite Postnikov system. Appeared in Contemporary Math. 181, (1995)