Phantom maps and torsion

AbstractFor 1-connected, finite type CW-spaces X and Y with Y a loop space, the group Ph(X, Y) of pointed homotopy classes of phantom maps from X to Y is divisible abelian. We obtain sharpened and generalized versions of examples demonstrating that the group Ph(X, Y) may possess torsion. Moreover, we give a complete and explicit description of those divisible abelian groups that may be realized as Ph(X, Y) for suitable X and Y