  In an attempt at explaining the observed neutrino mass-squared differences
and leptonic mixing, lepton mass matrices with zero textures have been widely
studied. In the weak basis where the charged lepton mass matrix is diagonal,
various neutrino mass matrices with two zeros have been shown to be consistent
with the current experimental data. Using the canonical and Smith normal form
methods, we construct the minimal Abelian symmetry realizations of these
phenomenological two-zero neutrino textures. The implementation of these
symmetries in the context of the seesaw mechanism for Majorana neutrino masses
is also discussed.
