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Frobenius Categories versus Brauer Blocks

- The Grothendieck Group of the Frobenius Category of a Brauer Block

  • Format
  • Bog, hardback
  • Engelsk

Beskrivelse

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 .

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Detaljer
  • SprogEngelsk
  • Sidetal498
  • Udgivelsesdato13-03-2009
  • ISBN139783764399979
  • Forlag Birkhauser Verlag Ag
  • FormatHardback
Størrelse og vægt
coffee cup img
10 cm
book img
15,5 cm
23,5 cm

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