  A group G is said to have the Magnus property if the following holds:
whenever two elements x,y have the same normal closure, then x is conjugate to
y or its inverse. We prove: Let p be an odd prime, and let G,H be residually
finite-p groups with the Magnus property. Then the direct product of G and H
has the Magnus property.
  By considering suitable crystallographic groups, we give an explicit example
of finitely generated, torsion-free, residually-finite groups G,H with the
Magnus property such that the direct product of G and H does not have the
Magnus property.
