2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/156852Let X be a proper hyperbolic geodesic metric space and let G be a closed subgroup of the isometry group Iso(X) of X. We show that if G is not amenable then its second continuous bounded cohomology group with coefficients the regular representation does not vanish. This yields some structure results for such groups.30 pages; writing improved, details added. Combined with parts of math.GR/0508532. To appear in GAFAGroup TheoryGeometric Topology22F50text