Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 364-385 |
| Seitenumfang | 22 |
| Fachzeitschrift | Journal of algebra |
| Jahrgang | 398 |
| Publikationsstatus | Veröffentlicht - 15 Jan. 2014 |
| Extern publiziert | Ja |
Abstract
For a p-block B of a finite group G with defect group D Olsson conjectured that k0(B) ≤ |D : D '|, where k0(B) is the number of characters in B of height 0 and D ' denotes the commutator subgroup of D. Brauer deduced Olsson's Conjecture in the case where D is a dihedral 2-group using the fact that certain algebraically conjugate subsections are also conjugate in G. We generalize Brauer's argument for arbitrary primes p and arbitrary defect groups. This extends two results by Robinson. For p > 3 we show that Olsson's Conjecture is satisfied for defect groups of p-rank 2 and for minimal non-abelian defect groups.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Algebra und Zahlentheorie
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in: Journal of algebra, Jahrgang 398, 15.01.2014, S. 364-385.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - A note on olsson's conjecture
AU - Héthelyi, Lászlo
AU - Külshammer, Burkhard
AU - Sambale, Benjamin
N1 - Funding Information: The first author was supported by an OTKA Grant (National Scientific Research Grant No. 77-476). The third author is supported by the “Deutsche Forschungsgemeinschaft”. We are grateful to the referee for some valuable comments.
PY - 2014/1/15
Y1 - 2014/1/15
N2 - For a p-block B of a finite group G with defect group D Olsson conjectured that k0(B) ≤ |D : D '|, where k0(B) is the number of characters in B of height 0 and D ' denotes the commutator subgroup of D. Brauer deduced Olsson's Conjecture in the case where D is a dihedral 2-group using the fact that certain algebraically conjugate subsections are also conjugate in G. We generalize Brauer's argument for arbitrary primes p and arbitrary defect groups. This extends two results by Robinson. For p > 3 we show that Olsson's Conjecture is satisfied for defect groups of p-rank 2 and for minimal non-abelian defect groups.
AB - For a p-block B of a finite group G with defect group D Olsson conjectured that k0(B) ≤ |D : D '|, where k0(B) is the number of characters in B of height 0 and D ' denotes the commutator subgroup of D. Brauer deduced Olsson's Conjecture in the case where D is a dihedral 2-group using the fact that certain algebraically conjugate subsections are also conjugate in G. We generalize Brauer's argument for arbitrary primes p and arbitrary defect groups. This extends two results by Robinson. For p > 3 we show that Olsson's Conjecture is satisfied for defect groups of p-rank 2 and for minimal non-abelian defect groups.
KW - Block
KW - Characters
KW - Defect group
KW - Height
KW - P-Rank
KW - Subsection
UR - http://www.scopus.com/inward/record.url?scp=84887140183&partnerID=8YFLogxK
U2 - 10.1016/j.jalgebra.2012.08.010
DO - 10.1016/j.jalgebra.2012.08.010
M3 - Article
AN - SCOPUS:84887140183
VL - 398
SP - 364
EP - 385
JO - Journal of algebra
JF - Journal of algebra
SN - 0021-8693
ER -