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We show that in an $SU(2)\otimes U(1)$ model with a DSF-like invisible axionit is possible to obtain (i) the convergence of the three gauge couplingconstants at an energy scale near the Peccei-Quinn scale; (ii) the correctvalue for $\sin^2\hat{\theta}_W(M_Z)$; (iii) the stabilization of the proton bythe cyclic $Z_{13}\otimes Z_3$ symmetries which also stabilize the axion as asolution to the strong CP problem. Concerning the convergence of the threecoupling constants and the prediction of the weak mixing angle at the $Z$-peak,this model is as good as the minimal supersymmetric standard model with$\mu_{\rm SUSY}=M_Z$. We also consider the standard model with six and sevenHiggs doublets. The main calculations were done in the 1-loop approximation butwe briefly consider the 2-loop contributions.Comment: 12 pages, 4 figure

Grand unification and proton stability near the Peccei-Quinn scale