  An example is given of a compact absolute retract that is not a Hilbert cube
manifold but whose second symmetric porduct is the Hilbert cube. A factor
theorem is given for nth symmetric product of the cartesian product of any
absolute neighborhood retract with the Hilbert cube. A short proof is included
of the known fact that symmetric products preserve the property of being a
compact Hilbert cube manifold (the theorem is proved here for all Hilbert cube
manifolds).
