  We show that by imposing local $Z_{13}\otimes Z_3$ symmetries in an
$SU(2)\otimes U(1)$ electroweak model we can implement an invisible axion in
such a way that (i) the Peccei-Quinn symmetry is an automatic symmetry of the
classical Lagrangian; and (ii) the axion is protected from semi classical
gravitational effects. In order to be able to implement such a large discrete
symmetry, and at the same time allow a general mixing in each charge sector, we
introduce right-handed neutrinos and enlarge the scalar sector of the model.
The domain wall problem is briefly considered.
