Geodesic
Quasi-isolated blocks and Brauer’s height zero conjecture
Radha Kessar1 ; Gunter Malle2
1 Department of Mathematics, City University London, Northampton Square, London EC1V 0HB, United Kingdom
2 Fachbereich Mathematik, TU Kaiserslautern, Postfach 3049, 67653 Kaisersautern, Germany
Annals of mathematics, Tome 178 (2013) no. 1, pp. 321-384.

Voir la notice de l'article provenant de la source Annals of Mathematics website

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 Knörr 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.
DOI : 10.4007/annals.2013.178.1.6

Radha Kessar 1 ; Gunter Malle 2

1 Department of Mathematics, City University London, Northampton Square, London EC1V 0HB, United Kingdom
2 Fachbereich Mathematik, TU Kaiserslautern, Postfach 3049, 67653 Kaisersautern, Germany 
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Radha Kessar; Gunter Malle. Quasi-isolated blocks and Brauer’s height zero conjecture. Annals of mathematics, Tome 178 (2013) no. 1, pp. 321-384. doi : 10.4007/annals.2013.178.1.6. http://geodesic.mathdoc.fr/articles/10.4007/annals.2013.178.1.6/

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