We consider a problem on the conditions of a compact Lie group G that the loop
space of the p–completed classifying space be a p–compact group for a set of primes.
In particular, we discuss the classifying spaces BG that are p–compact for all primes
when the groups are certain subgroups of simple Lie groups. A survey of the
p–compactness of BG for a single prime is included.
Keywords
p–compact group, classifying space,
p–completion, Lie group
