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The $D_4$ flavor model based on $mathrm{SU}(3)_C otimes mathrm{SU}(3)_L otimes mathrm{U}(1)_X$ gauge symmetry that aims at describing quark mass and mixing is updated. After spontaneous breaking of flavor symmetry, with the constraint on the Higgs vacuum expectation values (VEVs) in the Yukawa couplings, all of quarks have consistent masses, and a realistic quark mixing matrix can be realized at the first order of perturbation theory.
We construct a $D_4$ flavor model based on SU(3)_C X SU}(3_L X U(1)_X gauge symmetry responsible for fermion masses and mixings. The neutrinos get small masses from antisextets which are in a singlet and a doublet under $D_4$. If the D_4 symmetry is
We construct a 3-3-1 model based on non-Abelian discrete symmetry $T_7$ responsible for the fermion masses. Neutrinos get masses from only anti-sextets which are in triplets $underline{3}$ and $underline{3}^*$ under $T_7$. The flavor mixing patterns
We build the first 3-3-1 model based on the $Delta (27)$ discrete group symmetry, consistent with fermion masses and mixings. In the model under consideration, the neutrino masses are generated from a combination of type-I and type-II seesaw mechanis
A new S3 flavor model based on $mathrm{SU}(3)_C otimes mathrm{SU}(3)_L otimes mathrm{U}(1)_X$ gauge symmetry responsible for fermion masses and mixings different from our previous work is constructed. The new feature is a two - dimensional represen
We construct a 3-3-1 model based on family symmetry S_4 responsible for the neutrino and quark masses. The tribimaximal neutrino mixing and the diagonal quark mixing have been obtained. The new lepton charge mathcal{L} related to the ordinary lepton