{"product_id":"frobenius-categories-versus-brauer-blocks-von-lluis-puig","title":"Frobenius Categories versus Brauer Blocks","description":"\u003cp\u003eI1 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 .\u003c\/p\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783764399979\"\u003e\u003ch3\u003eThe Grothendieck Group of the Frobenius Category of a Brauer Block\u003c\/h3\u003e\u003c\/div\u003e","brand":"Autorenwelt Shop","offers":[{"title":"Hardcover - 9783764399979","offer_id":49592939315525,"sku":"9783764399979","price":128.39,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/8f486ef3-3fff-4816-b579-b68115ca6d1c.jpg?v=1774759701","url":"https:\/\/shop.autorenwelt.de\/en\/products\/frobenius-categories-versus-brauer-blocks-von-lluis-puig","provider":"Autorenwelt Shop","version":"1.0","type":"link"}