Modular Representation Theory of Blocks with Trivial Intersection Defect Groups
نویسندگان
چکیده
منابع مشابه
Modular Representation Theory of Blocks with Trivial Intersection Defect Groups
We show that Uno’s refinement of the projective conjecture of Dade holds for every block whose defect groups intersect trivially modulo the maximal normal p-subgroup. This corresponds to the block having p-local rank one as defined by Jianbei An and Eaton. An immediate consequence is that Dade’s projective conjecture, Robinson’s conjecture, Alperin’s weight conjecture, the Isaacs– Navarro conje...
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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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We consider p-blocks with abelian defect groups and in the first part prove a relationship between its Loewy length and that for blocks of normal subgroups of index p. Using this, we show that if B is a 2-block of a finite group with abelian defect group D ∼= C2a1 × · · · × C2ar × (C2), where ai > 1 for all i and r ≥ 0, then d < LL(B) ≤ 2a1 + · · · + 2ar + 2s − r + 1, where |D| = 2d. When s = 1...
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ژورنال
عنوان ژورنال: Algebras and Representation Theory
سال: 2005
ISSN: 1386-923X,1572-9079
DOI: 10.1007/s10468-005-8144-5