| Frobenius Categories Versus Brauer Blocks: The Grothendieck Group of the Frobenius Category of a Brauer Block 2009 Edition Contributor(s): Puig, Lluís (Author) |
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ISBN: 376439997X ISBN-13: 9783764399979 Publisher: Birkhauser OUR PRICE: $123.49 Product Type: Hardcover - Other Formats Published: March 2009 |
| Additional Information |
| BISAC Categories: - Mathematics | Group Theory - Mathematics | Topology - General - Mathematics | Algebra - Abstract |
| Dewey: 512 |
| LCCN: 2009921943 |
| Series: Progress in Mathematics |
| Physical Information: 1.2" H x 6.3" W x 9.2" (2.10 lbs) 508 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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 ." |