Radiative neutrino masses and exotic right-handed neutrinos.

We consider an extension of the standard electroweak model with three Higgs doublets and global $B-L$ and $\mathbb{Z}_3$ symmetries. Two of the scalar doublets are inert due to the $\mathbb{Z}_3$ symmetry. We calculated all the mass spectra in the scalar and lepton sectors and accommodate the leptonic mixing matrix as well. We also include an analysis of the scalar sector, showing that the potential is limited from below, and we obtain the masses of the scalar sector. Furthermore we consider the effects of the model on the anaomalous magnetic dipole of charged leptons and the $\mu\to e\gamma$ decay. We also present the SUSY version of the model with global $B-L$ and $\mathbb{Z}_3\otimes\mathbb{Z}^\prime_3$ symmetries.