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arXiv · 1412.7020

Cartan matrices and Brauer's k(B)-Conjecture IV

Benjamin Sambale
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Abstract

In this note we give applications of recent results coming mostly from the third paper of this series. It is shown that the number of irreducible characters in a $p$-block of a finite group with abelian defect group $D$ is bounded by $|D|$ (Brauer's $k(B)$-Conjecture) provided $D$ has no large elementary abelian direct summands. Moreover, we verify Brauer's $k(B)$-Conjecture for all blocks with minimal non-abelian defect groups. This extends previous results by various authors.

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Benjamin Sambale. 2014-12-22. Cartan matrices and Brauer's k(B)-Conjecture IV. https://arxiv.org/abs/1412.7020

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