2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67800We construct a connected finite loop space of rank 66 and dimension 1254 whose rational cohomology is not isomorphic as a graded vector space to the rational cohomology of any compact Lie group, hence providing a counterexample to a classical conjecture. Aided by machine calculation we verify that our counterexample is minimal, i.e., that any finite loop space of rank less than 66 is in fact rationally equivalent to a compact Lie group, extending the classical known bound of 5.8 pagesAlgebraic TopologyGeometric Topology55P35; 55P15, 55R35text