  We study the Z2 topologically ordered surface state of three-dimensional
bosonic SPT phases with the discrete symmetries G1 x G2. It has been argued
that the topologically ordered surface state cannot be realized on a purely
two-dimensional lattice model. We carefully examine the statement and show that
the surface state should break G2 if the symmetry G1 is gauged. This manifests
the conflict of the symmetry G1 and G2 on the surface of the three-dimensional
SPT phase. Given that there is no such phenomena in the purely two-dimensional
model, it signals that the symmetries are encoded anomalously on the surface of
the three-dimensional SPT phases and that the surface state can never be
realized on the purely two-dimensional models.
