Blocks of small defect

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On blocks with abelian defect groups of small rank

Let B be a p-block of a finite group with abelian defect group D. Suppose that D has no elementary abelian direct summand of order p. Then we show that B satisfies Brauer’s k(B)-Conjecture (i. e. k(B) ≤ |D|). Together with former results, it follows that Brauer’s k(B)-Conjecture holds for all blocks of defect at most 3. We also obtain some related results.

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ژورنال

عنوان ژورنال: Proceedings of the American Mathematical Society

سال: 1992

ISSN: 0002-9939

DOI: 10.1090/s0002-9939-1992-1070516-1