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Let B be a p-block of a finite group G with abelian defect group D such thatS\unlhd G, S'=S, G/Z(S)\le\Aut(S) and S/Z(S) is a sporadic simple group. Weshow that B is isotypic to its Brauer correspondent in N_G(D) in the sense ofBrou\'e. This has been done by [Rouquier, 1994] for principal blocks and itremains to deal with the non-principal blocks.

Brou\'e's isotypy conjecture for the sporadic groups and their covers and automorphism groups