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    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
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Frobenius Categories Versus Brauer Blocks: The Grothendieck Group of the Frobenius Category of a Brauer Block

Frobenius Categories Versus Brauer Blocks: The Grothendieck Group of the Frobenius Category of a Brauer Block

Puig, Lluís

Hardcover

Series: Progress in Mathematics, Book 274

AlgebraGeneral Mathematics

ISBN10: 376439997X
ISBN13: 9783764399979
Publisher: Birkhauser
Published: Mar 13 2009
Pages: 498
Weight: 2.10
Height: 1.20 Width: 6.30 Depth: 9.20
Language: English
I1 More than one hundred years ago, Georg Frobenius [26] proved his remarkable theorem a?rming that, for a primep and a ?nite groupG, if the quotient of the normalizer by the centralizer of anyp-subgroup ofG is a p-group then, up to a normal subgroup of order prime top, G is ap-group. Ofcourse, itwouldbeananachronismtopretendthatFrobenius, when doing this theorem, was thinking the category notedF in the sequel G where the objects are thep-subgroups ofG and the morphisms are the group homomorphisms between them which are induced by theG-conjugation. Yet Frobenius hypothesis is truly meaningful in this category. I2 Fifty years ago, John Thompson [57] built his seminal proof of the nilpotencyoftheso-called Frobeniuskernelofa FrobeniusgroupGwithar- ments at that time completely new which might be rewritten in terms ofF; indeed, some time later, following these kind of arguments, George G Glauberman [27] proved that, under some rather strong hypothesis onG, the normalizerNofasuitablenontrivial p-subgroup ofG controls fusion inG, which amounts to saying that the inclusionN?G induces an ? equivalence of categoriesF =F .

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