Open Access
April, 2017 Cartan matrices and Brauer's $k(B)$-conjecture IV
Benjamin SAMBALE
J. Math. Soc. Japan 69(2): 735-754 (April, 2017). DOI: 10.2969/jmsj/06920735


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.


Download Citation

Benjamin SAMBALE. "Cartan matrices and Brauer's $k(B)$-conjecture IV." J. Math. Soc. Japan 69 (2) 735 - 754, April, 2017.


Published: April, 2017
First available in Project Euclid: 20 April 2017

zbMATH: 06737032
MathSciNet: MR3638283
Digital Object Identifier: 10.2969/jmsj/06920735

Primary: 20C15
Secondary: 20C20

Keywords: abelian defect groups , blocks , Brauer's $k(B)$-conjecture , minimal non-abelian defect groups

Rights: Copyright © 2017 Mathematical Society of Japan

Vol.69 • No. 2 • April, 2017
Back to Top