Permutation symmetries and the fermion mass matrix

We consider SU(2)×U(1) gauge models with an additional global symmetry of ${\mathrm{S}}_n$ type. In particular, we study ${\mathrm{S}}_4$ symmetry for a six-quark—six-lepton standard model. We find that the Kobayashi-Maskawa matrix is completely determined and the mass of the $t$ quark is predicted. Some of the results persist in ${\mathrm{S}}_n$ applied to $n$ families. Restrictions on neutrino masses and mixings are given. Implications of $\mathrm{CP}$ and flavor nonconservation that arise in the neutral-Higgs-boson sector are discussed.