2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/224801We 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.This is the version published by Geometry & Topology Monographs on 29 January 2007Algebraic Topology55R35, 55P15, 55P60text