Fermion masses and anti-grand unification

We present an extension of the Standard Model (SM) without supersymmetry, which we use to calculate order of magnitude values for the elements of the mass matrices in the SM. In our model we can fit the 9 quark and lepton masses and 3 mixing angles using only 3 free parameters, with the overall mass scale set by the electroweak interaction. The specific model described here has the anti-grand unified gauge group SMG3 ⊗ U(1)f at high energies where SMG ≡ SU(3) ⊗ SU(2) ⊗ U(1) is the SM gauge group. The SM fermions are placed in representations of the full gauge group so that they do not produce any anomalies. It is pointed out that the same results can be obtained in an anomaly free SMG ⊗ U(1)3 model.