The existence of maximal and minimal mixing angles in the neutrino mixing
matrix motivates the search for extensions to the Standard Model that may
explain these angles. A previous study (C.I.Low and R.R.Volkas,
Phys.Rev.D68,033007(2003)), began a systematic search to find the minimal
extension to the Standard Model that explains these mixing angles. It was found
that in the minimal extensions to the Standard Model which allow neutrino
oscillations, discrete unbroken lepton family symmetries only generate neutrino
mixing matrices that are ruled out by experiment. This paper continues the
search by investigating all models with two or more Higgs doublets, and an
Abelian family symmetry. It is found that discrete Abelian family symmetries
permit, but cannot explain, maximal atmospheric mixing, however these models
can ensure theta_{13}=0.Comment: Minor modifications, references added, typos corrected. LaTeX, 16
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