Tri-bimaximal neutrino mixing and the family symmetry Z7 x Z3

The non-Abelian finite group PSL2(7) is the only simple subgroup of SU(3) with a complex three-dimensional irreducible representation. It has two maximal subgroups, S-4 which, along with its own A(4) subgroup, has been successfully applied in numerous models of flavor, as well as the 21 element Frobenius group Z(7) x Z(3), which has gained much less attention. We show that it can also be used to generate tri-bimaximal mixing in the neutrino sector, while allowing for quark and charged lepton hierarchies. (c) 2007 Elsevier B.V. All rights reserved.