  We show that the Standard Model Lagrangian, including small neutrino masses,
has an anomaly-free discrete Z_6 symmetry. Anomaly cancellation requires the
number of family to be 3 mod 6. This symmetry can ensure the stability of the
nucleon even when the threshold of new physics \Lambda is low as 10^2 GeV. All
\Delta B=1 and \Delta B=2 (B is the baryon number) effective operators are
forbidden by the Z_6 symmetry. \Delta B=3 operators are allowed, but they arise
only at dimension 15. We suggest a simple mechanism for realizing reasonable
neutrino masses and mixings even with such a low scale for \Lambda.
