The Chase radical and reduced products

Let κ be a regular uncountable cardinal. We shall give a criterion for certain reduced products image of torsion-free abelian groups image to be aleph, Hebrew1-free. As an application we shall show that the norm of the Chase radical is aleph, Hebrew1 in ZFC, a result which was previously known only under the assumption of the continuum hypothesis 2aleph, Hebrew0=aleph, Hebrew1.