Birkhäuser
Frobenius Categories Versus Brauer Blocks: The Grothendieck Group of the Frobenius Category of a Brauer Block
Product Code:
9783764399979
ISBN13:
9783764399979
Condition:
New
$139.06
Frobenius Categories Versus Brauer Blocks: The Grothendieck Group of the Frobenius Category of a Brauer Block
$139.06
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 ."
| Author: Llu? Puig |
| Publisher: Birkhauser |
| Publication Date: Mar 13, 2009 |
| Number of Pages: 498 pages |
| Binding: Hardback or Cased Book |
| ISBN-10: 376439997X |
| ISBN-13: 9783764399979 |
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