Quasi-isolated blocks and Brauer's height zero conjecture
- 1 July 2013
- journal article
- research article
- Published by Annals of Mathematics in Annals of Mathematics
- Vol. 178 (1), 321-384
- https://doi.org/10.4007/annals.2013.178.1.6
Abstract
This paper has two main results. Firstly, we complete the parametrisation of all p-blocks of finite quasi-simple groups by finding the so-called quasi-isolated blocks of exceptional groups of Lie type for bad primes. This relies on the explicit decomposition of Lusztig induction from suitable Levi subgroups. Our second major result is the proof of one direction of Brauer's long-standing height zero conjecture on blocks of finite groups, using the reduction by Berger and Knorr to the quasi-simple situation. We also use our result on blocks to verify a conjecture of Malle and Navarro on nilpotent blocks for all quasi-simple groups.Keywords
This publication has 34 references indexed in Scilit:
- Sur les l-blocs unipotents des groupes réductifs finis quand l est mauvaisJournal of Algebra, 2000
- On Blocks of Finite Reductive Groups and Twisted InductionAdvances in Mathematics, 1999
- Brauer's Height Zero Conjecture for Central Quotients of Special Linear and Special Unitary GroupsJournal of Algebra, 1999
- On unipotent blocks and their ordinary charactersInventiones Mathematicae, 1994
- Die unipotenten charaktere von 2F4(q2)Communications in Algebra, 1990
- The blocks of finite classical groups.Journal für die reine und angewandte Mathematik (Crelles Journal), 1989
- The blocks of finite general linear and unitary groupsInventiones Mathematicae, 1982
- Defect groups for finite groups of Lie typeMathematische Zeitschrift, 1971
- On Ree’s series of simple groupsTransactions of the American Mathematical Society, 1966
- Investigations on Group CharactersAnnals of Mathematics, 1941