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We study a neutrino model introducing an additional nontrivial gauged lepton symmetry where the neutrino masses are induced at two-loop level while the first and second charged-leptons of the standard model are done at one-loop level. As a result of model structure, we can predict one massless active neutrino, and there is a dark matter candidate. Then we discuss neutrino mass matrix, muon anomalous magnetic moment, lepton flavor violations, oblique parameters, and relic density of dark matter taking into account the experimental constraints.

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