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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 insuch a way that (i) the Peccei-Quinn symmetry is an automatic symmetry of theclassical Lagrangian; and (ii) the axion is protected from semi classicalgravitational effects. In order to be able to implement such a large discretesymmetry, and at the same time allow a general mixing in each charge sector, weintroduce right-handed neutrinos and enlarge the scalar sector of the model.The domain wall problem is briefly considered.Comment: PQ charges and typos correcte

Naturally light invisible axion and local Z13⊗Z3 symmetries