Details
| Original language | English |
|---|---|
| Pages (from-to) | 735-754 |
| Number of pages | 20 |
| Journal | Journal of the Mathematical Society of Japan |
| Volume | 69 |
| Issue number | 2 |
| Publication status | Published - 2017 |
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.
Keywords
- Abelian defect groups, Blocks, Brauer's k(B)-conjecture, Minimal non-abelian defect groups
ASJC Scopus subject areas
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In: Journal of the Mathematical Society of Japan, Vol. 69, No. 2, 2017, p. 735-754.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Cartan matrices and Brauer's k(B)-conjecture IV
AU - Sambale, Benjamin
N1 - Publisher Copyright: © 2017 The Mathematical Society of Japan.
PY - 2017
Y1 - 2017
N2 - 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.
AB - 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.
KW - Abelian defect groups
KW - Blocks
KW - Brauer's k(B)-conjecture
KW - Minimal non-abelian defect groups
UR - http://www.scopus.com/inward/record.url?scp=85019201210&partnerID=8YFLogxK
U2 - 10.2969/jmsj/06920735
DO - 10.2969/jmsj/06920735
M3 - Article
AN - SCOPUS:85019201210
VL - 69
SP - 735
EP - 754
JO - Journal of the Mathematical Society of Japan
JF - Journal of the Mathematical Society of Japan
SN - 0025-5645
IS - 2
ER -