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

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Preprint
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DOI: 10.1142/S0218196715500277
arXiv ID: 1504.01856
Source
arXiv
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Abstract

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

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