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We contribute to the classification of finite dimensional algebras understable equivalence of Morita type. More precisely we give a classification ofthe class of Erdmann's algebras of dihedral, semi-dihedral and quaternion typeand obtain as byproduct the validity of the Auslander-Reiten conjecture forthese classes of algebras.

Classifying tame blocks and related algebras up to stable equivalences of Morita type