{"product_id":"frobenius-categories-versus-brauer-blocks-the-grothendieck-group-of-the-frobenius-category-of-a-brauer-block-progress-in-mathematics-274-376439997x","title":"Frobenius Categories versus Brauer Blocks: The Grothendieck Group of the Frobenius Category of a Brauer Block (Progress in Mathematics, 274)","description":"\u003cp\u003e\u003cstrong\u003eISBN:\u003c\/strong\u003e 376439997X\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eAuthor:\u003c\/strong\u003e Puig, Llu\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eCondition:\u003c\/strong\u003e New\u003c\/p\u003e\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","brand":"Mia Karts","offers":[{"title":"Default Title","offer_id":51873623769376,"sku":"NEW376439997X","price":128.58,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0980\/7426\/3840\/files\/617aDfqYfOL.jpg?v=1781721439","url":"https:\/\/miakarts.com\/products\/frobenius-categories-versus-brauer-blocks-the-grothendieck-group-of-the-frobenius-category-of-a-brauer-block-progress-in-mathematics-274-376439997x","provider":"Miakarts Books","version":"1.0","type":"link"}