Abstract
Broué conjectures that a block of a finite group G with abelian defect group P is Rickard equivalent to its Brauer correspondent in the normalizer NG(P). We find a character-theoretic criterion on extensions of Rickard equivalences between blocks. As an application, we prove that the conjecture holds for the principal block of a finite group with abelian defect group and cyclic hyperfocal subgroup.
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