 
Summary: pCOMPACT GROUPS AS SUBGROUPS
OF MAXIMAL RANK OF KACMOODY GROUPS
JAUME AGUAD´E
1. Introduction
In [28], Kitchloo constructed a map f : BX BK
p where K is a certain Kac
Moody group of rank two, X is a rank two mod p finite loop space and f is such
that it induces an isomorphism between even dimensional mod p cohomology groups.
Here B denotes the classifying space functor and ()
p denotes the BousfieldKan
Fpcompletion functor ([8]).
This space X or rather the triple (X
p , BX
p , e) where e : X BX is a
particular example of what is known as a pcompact group. These objects were
introduced by Dwyer and Wilkerson in [15] as the homotopy theoretical framework
to study finite loop spaces and compact Lie groups from a homotopy point of view.
The foundational paper [15] together with its many sequels by DwyerWilkerson and
other authors represent now an active, well established research area which contains
some of the most important recent advances in homotopy theory.
