Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 421-433 |
| Seitenumfang | 13 |
| Fachzeitschrift | Vietnam Journal of Mathematics |
| Jahrgang | 52 |
| Ausgabenummer | 2 |
| Frühes Online-Datum | 8 Mai 2023 |
| Publikationsstatus | Veröffentlicht - Apr. 2024 |
Abstract
We prove that the number of irreducible real characters in a nilpotent block of a finite group is locally determined. We further conjecture that the Frobenius–Schur indicators of those characters can be computed for p=2 in terms of the extended defect group. We derive this from a more general conjecture on the Frobenius–Schur indicator of projective indecomposable characters of 2-blocks with one simple module. This extends results of Murray on 2-blocks with cyclic and dihedral defect groups.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Allgemeine Mathematik
Zitieren
- Standard
- Harvard
- Apa
- Vancouver
- BibTex
- RIS
in: Vietnam Journal of Mathematics, Jahrgang 52, Nr. 2, 04.2024, S. 421-433.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Real Characters in Nilpotent Blocks
AU - Sambale, Benjamin
N1 - Funding Information: The work is supported by the German Research Foundation (SA 2864/3-1 and SA 2864/4-1).
PY - 2024/4
Y1 - 2024/4
N2 - We prove that the number of irreducible real characters in a nilpotent block of a finite group is locally determined. We further conjecture that the Frobenius–Schur indicators of those characters can be computed for p=2 in terms of the extended defect group. We derive this from a more general conjecture on the Frobenius–Schur indicator of projective indecomposable characters of 2-blocks with one simple module. This extends results of Murray on 2-blocks with cyclic and dihedral defect groups.
AB - We prove that the number of irreducible real characters in a nilpotent block of a finite group is locally determined. We further conjecture that the Frobenius–Schur indicators of those characters can be computed for p=2 in terms of the extended defect group. We derive this from a more general conjecture on the Frobenius–Schur indicator of projective indecomposable characters of 2-blocks with one simple module. This extends results of Murray on 2-blocks with cyclic and dihedral defect groups.
KW - 20C15
KW - 20C20
KW - Frobenius–Schur indicators
KW - Nilpotent blocks
KW - Real characters
UR - http://www.scopus.com/inward/record.url?scp=85158103368&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2301.13440
DO - 10.48550/arXiv.2301.13440
M3 - Article
AN - SCOPUS:85158103368
VL - 52
SP - 421
EP - 433
JO - Vietnam Journal of Mathematics
JF - Vietnam Journal of Mathematics
SN - 2305-221X
IS - 2
ER -