Abstract
It is shown how to obtain recently-proposed two-zero Majorana mass textures in models with three Higgs triplets with small VEVs and a sufficiently massive triplet Majoron by using abelian discrete symmetries. It is briefly discussed how in SU(5) grand unification where the triplets occur in {\bf 15}'s the neutrino textures can be related to up- and down- quark mass textures.
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