Pairings of $p$-Compact Groups and $H$-Structures on the Classifying Spaces of Finite Loop Spaces

Abstract

We consider the maps between classifying spaces of /7-compact groups of the form BX x B Y -* BZ. The main theorem shows that if the restriction map on B Y is a weak epimorphism, then the restriction on BX should factor through the classifying spaces of the center of the /7-compact group Z.