Minimal semi-annihilating ZN scalar dark matter

We study the dark matter from an inert doublet and a complex scalar singlet stabilized by Z(N) symmetries. This field content is the minimal one that allows dimensionless semi-annihilation couplings for N > 2. We consider explicitly the Z(3) and Z(4) cases and take into account constraints from perturbativity, unitarity, vacuum stability, necessity for the electroweak Z(N) preserving vacuum to be the global minimum, electroweak precision tests, upper limits from direct detection and properties of the Higgs boson. Co-annihilation and semi-annihilation of dark sector particles as well as dark matter conversion significantly modify the cosmic abundance and direct detection phenomenology.