Broué's isotypy conjecture for the sporadic groups and their covers and automorphism groups
Abstract
Let B be a p-block of a finite group G with abelian defect group D such that S ≤ G ≤ Aut(S), S′ = S and S/Z(S) is a sporadic simple group. We show that B is isotypic to its Brauer correspondent in NG(D) in the sense of Broué. This has been done by Rouquier for principal blocks and it remains to deal with the non-principal blocks.
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