Induced QCD and hidden localZNsymmetry

We show that a lattice model for induced lattice QCD which was recently proposed by Kazakov and Migdal has a ${\mathrm{Z}}_{\mathit{N}}$ gauge symmetry which, in the strong coupling phase, results in a local confinement where only color singlets are allowed to propagate along links and all Wilson loops for nonsinglets average to zero. We argue that if this model is to give QCD in its continuum limit, it must have a phase transition. We give arguments to support the presence of such a phase transition.