Details
Originalsprache | Englisch |
---|---|
Seiten (von - bis) | 735-754 |
Seitenumfang | 20 |
Fachzeitschrift | Journal of the Mathematical Society of Japan |
Jahrgang | 69 |
Ausgabenummer | 2 |
Publikationsstatus | Veröffentlicht - 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.
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in: Journal of the Mathematical Society of Japan, Jahrgang 69, Nr. 2, 2017, S. 735-754.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › 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 -