Splitting of three nearly mass-degenerate neutrinos

Assuming the canonical seesaw mechanism together with an SO(3) family symmetry for leptons, broken only by the charged-lepton masses, I show that the three neutrinos of Majorana mass m0 are split radiatively in two loops by a maximum finite calculable amount of order 10−9 m0. This is very suitable for dark matter and vacuum solar neutrino oscillations. I also discuss how atmospheric neutrino oscillations can be incorporated.