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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We classify those finite simple groups whose Brauer graph (or decomposition matrix) has a p-block with defect 0, completing an investigation of many authors. The only finite simple groups whose defect zero p−blocks remained unclassified were the alternating groups An. Here we show that these all have a p-block with defect 0 for every prime p ≥ 5. This follows from proving the same result for ev...
متن کاملOn defect groups for generalized blocks of the symmetric group
In a paper of 2003, B. Külshammer, J. B. Olsson and G. R. Robinson defined l-blocks for the symmetric groups, where l > 1 is an arbitrary integer. In this paper, we give a definition for the defect group of the principal l-block. We then check that, in the Abelian case, we have an analogue of one of M. Broué’s conjectures.
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ژورنال
عنوان ژورنال: Mathematische Zeitschrift
سال: 2004
ISSN: 0025-5874,1432-1823
DOI: 10.1007/s00209-003-0545-8