  We consider the phenomenology of the gauged abelian symmetry B + 3 (L_e -
L_mu - L_tau). Right-handed neutrinos necessary to cancel triangle anomalies
are used in a type-I seesaw scheme to create active neutrino masses. Breaking
the B + 3 (L_e - L_mu - L_tau) symmetry spontaneously below the seesaw scale
generates low energy neutrino mass matrices with the approximate symmetries L_e
(leading to normal hierarchy) or L_e - L_mu - L_tau (inverted hierarchy). For
the latter we need to introduce a Z_2 symmetry which decouples one of the
right-handed neutrinos. If exact, this Z_2 leads to a Majorana dark matter
candidate that interacts with the Standard Model via the Z' and a scalar s
originating from spontaneous breaking of the new symmetry. The measured relic
abundance of the dark matter particle can be obtained around the scalar and Z'
resonances, while direct detection experiments are mainly sensitive to scalar
exchange, which is induced by mass mixing of s with the standard Higgs.
