Abelian discrete symmetries ZN and ZnR from string orbifolds

We show that Abelian discrete symmetries ZN and ZnR from string orbifolds result by assigning vacuum expectation values (VEVs) only to specified singlets. These singlets obtaining VEVs carry the gauge charges (of the covering U(1) gauge group) as multiples of N for ZN and n for ZnR. We explicitly show this realization in a Z12−I orbifold model.