The Peccei-Quinn symmetry is an automatic symmetry of the 3-3-1 gauge models which, consequently are not plagued with the strong CP problem. Nevertheless, the axion that emerges from spontaneous breaking of Peccei-Quinn symmetry cannot be made invisible in the original versions of these models, unless we extend their scalar sector by an additional neutral scalar singlet. In this case we show that if, we also add heavy neutrinos in the singlet form, we get to solve three interesting open

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... s at once: the real component of the neutral scalar singlet driving inflation, the axion playing the role of the dark matter of the universe and standard neutrinos gaining masses through seesaw mechanism.