Remarks on neutrino mass and magnetic moment

A neutrino magnetic moment of the order of 10(-11)mu(B) and a naturally small mass within the framework of the modified Zee model have been calculated. These values are consistent with the observed ones. A model for Majorana neutrinos with a Voloshin-type SU(2) horizontal symmetry that protects the masses but not magnetic moments has been constructed. This symmetry is broken only by terms of order g(W) m(mu)-m(e)/2M(W) approximate to 4x10(-3) resulting in masses which are naturally small of the order of eV. The difference between the electron and muon lepton numbers is conserved so that rare processes like mu --> e gamma, mu --> eee and neutrinoless double-beta decays are forbidden.