Quasi-isolated blocks and Brauer’s height zero conjecture


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.


Radha Kessar

Department of Mathematics, City University London, Northampton Square, London EC1V 0HB, United Kingdom

Gunter Malle

Fachbereich Mathematik, TU Kaiserslautern, Postfach 3049, 67653 Kaisersautern, Germany