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arXiv · 1709.05068

On a minimal counterexample to Brauer's $k(B)$-conjecture

Gunter Malle
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Abstract

We study Brauer's long-standing $k(B)$-conjecture on the number of characters in $p$-blocks for finite quasi-simple groups and show that their blocks do not occur as a minimal counterexample for $p\ge5$ nor in the case of abelian defect. For $p=3$ we obtain that the principal 3-blocks do not provide minimal counterexamples. We also determine the precise number of irreducible characters in unipotent blocks of classical groups for odd primes.

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Gunter Malle. 2017-09-15. On a minimal counterexample to Brauer's $k(B)$-conjecture. https://arxiv.org/abs/1709.05068

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