RESIDUAL DISCRETE SYMMETRY AND SU(8) GRAND UNIFIED MODEL

It is pointed out that there exists a residual diserete symmetry when the grand unifiedgauge group SU(N) is broken down to G_1=SU(3)×SU(2)×U(1) at the mass scale of theorder of 10~(15)GeV through a concrete Higgs mechanism, This residual symmetry prevents somefermions from receiving masses of that order, so that the gaugo group can accommodate morelow mass fermions. We have proved a theorem connected with the residual symmetry and gota new criterion for constructing SU(N) grand unified models. Basing ourselves on thiscriterion we discuss concretely an SU(8) grand unified model accommodating three genera-tions with V-A coupling. In this model the Higgs mechanism of spontaneous breaking and thefermion mass matrices are presented.