Subject: Question for the discussion list Date: Thu, 8 Mar 2001 12:49:14 -0500 From: Allen Hatcher Question: Does anyone know an example of a space with finite homotopy groups but some homology group infinite? (Not H_0 of course!) Comments: Serre theory says the example can't be simply-connected. A transfer argument with the universal cover shows that the homology groups must be torsion groups, so an infinite homology group couldn't be finitely generated. The example can't be a K(G,1) since finite groups have finite homology groups. Allen Hatcher