Categorically Equivalent and Isotypic Blocks Original Research Article

Let N be a normal subgroup of the finite group G such that G = NCG(D) where D set membership, variant Sylp (N). Let (O, K, k) be a p-modular system that is "big enough," let f be the principal block idempotent of Z(ON), and let e be a block idempotent of Z(OG) that covers f and such that D is a defect group of e. Then the categories mod - e(OG) and mod - f(ON) are equivalent, e is of principal type, and the pairs (G, e) and (N, f) are of the same type.