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It is well-known that the space group selection rule constrains theinteractions of closed strings on orbifolds. For some examples, this rule hasbeen described by an effective Abelian symmetry that combines with apermutation symmetry to a non-Abelian flavor symmetry like $D_4$ or$\Delta(54)$. However, the general case of the effective Abelian symmetries wasnot yet fully understood. In this work, we formalize the computation of theAbelian symmetry that results from the space group selection rule by imposingtwo conditions only: (i) well-defined discrete charges and (ii) theirconservation. The resulting symmetry, which we call the space group flavorsymmetry $D_S$, is uniquely specified by the Abelianization of the space group.For all Abelian orbifolds with $N=1$ supersymmetry we compute $D_S$ andidentify new cases, for example, where $D_S$ contains a $Z_2$ darkmatter-parity with charges 0 and 1 for massless and massive strings,respectively.

Note on the space group selection rule for closed strings on orbifolds