Quasi-isolated blocks and Brauer's height zero conjecture

Kessar, R. & Malle, G. (2013). Quasi-isolated blocks and Brauer's height zero conjecture. ANNALS OF MATHEMATICS, 178(1), pp. 321-384. doi: 10.4007/annals.2013.178.1.6

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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 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.

Item Type: Article
Additional Information: Published in ANNALS OF MATHEMATICS 2013
Uncontrolled Keywords: Brauer's height 0 conjecture, classification of blocks, isolated blocks, Lusztig induction
Subjects: Q Science > QA Mathematics
Divisions: School of Engineering & Mathematical Sciences
URI: http://openaccess.city.ac.uk/id/eprint/6908

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