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We propose an SU(5) grand unified model with an invisible axion and theunification of the three coupling constants which is in agreement with thevalues, at $M_Z$, of $\alpha$, $\alpha_s$, and $\sin^2\theta_W$. A discrete,anomalous, $Z_{13}$ symmetry implies that the Peccei-Quinn symmetry is anautomatic symmetry of the classical Lagrangian protecting, at the same time,the invisible axion against possible semi-classical gravity effects. Althoughthe unification scale is of the order of the Peccei-Quinn scale the proton isstabilized by the fact that in this model the standard model fields form theSU(5) multiplets completed by new exotic fields and, also, because it isprotected by the $Z_{13}$ symmetry.

An SU(5)$\otimes$Z_{13} Grand Unification Model