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 $p$-compact groups of the form $BX\times BY\to BZ$. The main theorem shows that if the restriction map on $BY$ is a weak epimorphism, then the restriction on $BX$ should factor through the classifying spaces of the center of the $p$-compact group $Z$.