Pairings of p-compact groups
and H-structures on the classifying spaces of finite loop spaces
Kenshi Ishiguro
Fukuoka University, Fukuoka 814-80, Japan
We consider the maps between classifying spaces
of p-compact groups of the form
$BX \times BY @>>> BZ$. 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. An application implies that,
for a finite loop space X, its classifying space
BX is an H-space (Hopf space) if and only if
X is the product of a torus and a finite abelian group.
It is also shown, for a compact Lie group G, exactly when
the p-completed space $(BG)\p$ has an H-structure.