  We present simple and predictive realizations of neutrino masses in theories
based on the $SU(6)$ grand unifying group. At the level of the lowest-dimension
operators, this class of models predicts a skew-symmetric flavor structure for
the Dirac mass term of the neutrinos. In the case that neutrinos are Dirac
particles, the lowest-order prediction of this construction is then one
massless neutrino and two degenerate massive neutrinos. Higher-dimensional
operators suppressed by the Planck scale perturb this spectrum, allowing a good
fit to the observed neutrino mass matrix. A firm prediction of this
construction is an inverted neutrino mass spectrum with the lightest neutrino
hierarchically lighter than the other two, so that the sum of neutrino masses
lies close to the lower bound for an inverted hierarchy. In the alternate case
that neutrinos are Majorana particles, the mass spectrum can be either normal
or inverted. However, the lightest neutrino is once again hierarchically
lighter than the other two, so that the sum of neutrino masses is predicted to
lie close to the corresponding lower bound for the normal or inverted
hierarchy. Near future cosmological measurements will be able to test the
predictions of this scenario for the sum of neutrino masses. In the case of
Majorana neutrinos that exhibit an inverted hierarchy, future neutrinoless
double beta experiments can provide a complementary probe.
