  Augmenting the Standard Model by three right-handed neutrinos allows for an
anomaly-free gauge group extension G_max = U(1)_(B-L) x U(1)_(L_e-L_mu) x
U(1)_(L_mu-L_tau). While simple U(1) subgroups of G_max have already been
discussed in the context of approximate flavor symmetries, we show how two-zero
textures in the right-handed neutrino Majorana mass matrix can be enforced by
the flavor symmetry, which is spontaneously broken very economically by singlet
scalars. These zeros lead to two vanishing minors in the low-energy neutrino
mass matrix after the seesaw mechanism. This study may provide a new testing
ground for a zero-texture approach: the different classes of two-zero textures
with almost identical neutrino oscillation phenomenology can in principle be
distinguished by their different Z' interactions at colliders.
