Journal Article

Characters of Positive Height in Blocks of Finite Quasi-Simple Groups

Olivier Brunat and Gunter Malle

in International Mathematics Research Notices

Volume 2015, issue 17, pages 7763-7786
Published in print January 2015 | ISSN: 1073-7928
Published online October 2014 | e-ISSN: 1687-0247 | DOI: http://dx.doi.org/10.1093/imrn/rnu171
Characters of Positive Height in Blocks of Finite Quasi-Simple Groups

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Eaton and Moretó proposed an extension of Brauer's famous height zero conjecture on blocks of finite groups to the case of nonabelian defect groups, which predicts the smallest nonzero height in such blocks in terms of local data. We show that their conjecture holds for principal blocks of quasi-simple groups, for all blocks of finite reductive groups in their defining characteristic, as well as for all covering groups of symmetric and alternating groups. For the proof, we determine the minimal nontrivial character degrees of Sylow [math]-subgroups of finite reductive groups in characteristic [math]. We provide some further evidence for blocks of groups of Lie type considered in cross characteristic.

Journal Article.  11098 words. 

Subjects: Mathematics

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