Symmetries of the Standard Model without and with a Right-Handed Neutrino

Given the particle content of the standard model without and with a right-handed neutrino, the requirement that all anomalies cancel singles out a set of possible global symmetries which can be gauged. I review this topic and propose a new gauge symmetry B - 3L_tau in the context of the minimal standard model consisting of the usual three families of quarks and leptons plus just one nu_R. The many interesting phenomenological consequences of this hypothesis are briefly discussed.