Frobenius Categories versus Brauer Blocks - The Grothendieck Group of the Frobenius Category of a Brauer Block (Hardcover, 2009 ed.)

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 .

General

Imprint:	Birkhauser Verlag AG
Country of origin:	Switzerland
Series:	Progress in Mathematics, 274
Release date:	March 2009
First published:	2009
Authors:	Lluis Puig
Dimensions:	235 x 155 x 30mm (L x W x T)
Format:	Hardcover
Pages:	498
Edition:	2009 ed.
ISBN-13:	978-3-7643-9997-9
Categories:	Books > Science & Mathematics > Mathematics > Topology > Algebraic topology
LSN:	3-7643-9997-X
Barcode:	9783764399979

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