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Duality maps of finite abelian groups are classified. As a corollary, spin models on finite abelian groups which arise from thesolutionsof the modular invariance equations are determined as tensor products of indecomposable spin models. We also classify finite abelian groups whose Bose-Mesner algebra can be generated by a spin model.

Duality Maps of Finite Abelian Groups and Their Applications to Spin Models