SIMPLE NON-ABELIAN FINITE FLAVOR GROUPS AND FERMION MASSES

The use of non-Abelian discrete groups G as family symmetries is discussed in detail. Out of all such groups up to order g = 31, the most appealing candidates are two subgroups of SU(2): the dicyclic (double dihedral) group G = Q(6) = ((d))D-3 (g = 12) and the double tetrahedral group ((d))T = Q(4) (x) over tilde Z(3) (g = 24) Both can allow a hierarchy t > b, tau > c > s, mu > u, d, e. The top quark is uniquely allowed to have a G symmetric mass. Sequential breaking of G and radiative corrections give the smaller masses. Anomaly freedom for gauging G subset of SU(2) is a strong constraint in assignment of fermions to representations of G.