RESUMEN

In the Standard Model, analogous fermions in different generations, say u,c and t or d,s and b, have completely identical couplings to all gauge bosons of the strong, weak and electromagnetic interactions. Prior to the introduction of a flavor singlet Higgs boson and mass terms, the Lagrangian is chiral and invariant with respect to any permutation of the left and right quark fields. In the first two of a series of papers, we considered the case when the flavor permutational symmetry S_{L}(3)xS_{R}(3) is explicitly broken to the groups S_{L}(2)xS_{R}(2) to nothing, giving rise to modified Fritszch mass matrices M_d and M_u. We obtained a very good chi^2 fit of the quark mixing matrix V^{th}_{CKM} to the experimentally determined V^{exp}_{CKM}. For the three inner angles alpha, beta and gamma of the unitarity triangle, we get, alpha=83 degrees, beta=22.1 degrees, gamma=75 degrees in good agreement with current data on CP violation. Recently with the aim of dealing with masses, mixings and CP violation in both the quark and lepton sectors on the same foothing, we proposed S(3) as a fundamental symmetry in the matter sector of the S.M.. In consequence, assuming that the lepton, quark and Higgs fields belong to the three-dimensional reducible representation of the permutation group S(3), we suggest a minimal S(3) invariant extension of the Standard Model. We find that in the leptonic sector the exact S(3)xZ_2 symmetry, which allows 6 real independent parameters, is consistent with experimental data and predicts the bi-maximal mixing of the left-handed neutrinos and that the third neutrino is the lightest neutrino. Z_2 is anomaly-free, but forbids CP-violations in the leptonic as well as in the hadronic sector. Therefore, we may identify the origin of the CP-violations with the breaking of the Z_2 symmetry, which may be understood in a more fundamental theory. With the exact S(3) only, there are 10 real independent parameters and one independent phase, which the Cabibbo-Kobayashi-Maskawa mixing matrix V_{CKM} depends on. A set of values of these parameters that are consistent with the experimental observations is given.