Untersuchungen zu Donovans Vermutung für klassische Gruppen

In 1980, Donovan conjectured that the number of Morita equivalence classes ofblocks of finite groups with prescribed defect group is finite. In this thesisDonovan's conjecture is investigated for classical groups. First, a recenttheorem of Bonnafe and Rouquier is used to reduce Donovan'sconjecture for classical groups to unipotent and isolated blocks. This isachieved by describing the conjugacy classes of semisimple elements and theircentralizers. It is shown that any isolated block of a classical group inunitary characteristic is Morita equivalent to a block of a group of the sametype whose dimension is bound in terms of the defect of the block, provided allcharacters in the block have non-degenerate Jordan correspondents. Assuming acompatibility condition for Jordan correspondence of characters, it is provedthat Donovan's conjecture holds for all blocks of classical groups in linearcharacteristic. Both results are proved using the corresponding results of Hißand Kessar on unipotent blocks via Jordan decomposition of characters.

Grantor dc:publisher

Publikationsserver der RWTH Aachen University

Year dc:date

2005

Author dc:creator

• Waldmüller, Reinhard

Contributors dc:contributor

• Hiß, Gerhard

• info:eu-repo/classification/ddc/510
• Mathematik
• Donovans Vermutung
• klassische Gruppen
• Zentralisatoren halbeinfacher Elemente
• isolierte Blöcke

Statement dc:rights

• info:eu-repo/semantics/openAccess

Language dc:language

ger

Identifier

https://publications.rwth-aachen.de/search?p=id:%22RWTH-CONV-122052%22

OAI identifier oai:identifier

oai:publications.rwth-aachen.de:60333