Fermion masses and mixings in a flavour symmetric GUT

We describe a supersymmetric Grand Unified Theory based on the gauge group $\text{SU}(5{)}^3$, or $\text{SO}(10{)}^3$, invariant under the interchange of any~SU(5), or~SO(10), with each family multiplet transforming non trivially under one different individual group factor. A realistic pattern of fermion masses and mixings is obtained as a result of an appropriate choice out of the many possible discretely degenerate vacua of the theory. In the~SO(10) case, we predict the three neutrino masses in terms of an overall scale and, within factors of order unity, their mixing angles. A ${\nu }_e$-${\nu }_{\mu }$ oscillation is suggested as a solution of the solar neutrino problem, implying a visible ${\nu }_{\mu }$-${\nu }_{\tau }$ oscillation in the forthcoming experiments. Grand unified theories of this type could be obtainable in a string theory framework.