Details
| Original language | English |
|---|---|
| Article number | 14 |
| Pages (from-to) | 243-260 |
| Number of pages | 18 |
| Journal | Publicationes mathematicae |
| Volume | 99 |
| Issue number | 1-2 |
| Publication status | Published - 2021 |
Abstract
For a finite group G, we investigate the smallest positive integer e(G) such that the map sending g ∈ G to e(G)|G : CG(g)| is a generalized character of G. It turns out that e(G) is strongly influenced by local data, but behaves irregularly for non-abelian simple groups. We interpret e(G) as an elementary divisor of a certain non-negative integral matrix related to the character table of G. Our methods applied to Brauer characters also answer a recent question of Navarro: The p-Brauer character table of G determines |G|p0.
Keywords
- Conjugation action, Generalized character
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
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In: Publicationes mathematicae, Vol. 99, No. 1-2, 14, 2021, p. 243-260.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - The reciprocal character of the conjugation action
AU - Sambale, Benjamin
N1 - Funding Information: Mathematics Subject Classification: 20C15, 20C20. Key words and phrases: conjugation action, generalized character. The work is supported by the German Research Foundation (SA 2864/1-2 and SA 2864/3-1).
PY - 2021
Y1 - 2021
N2 - For a finite group G, we investigate the smallest positive integer e(G) such that the map sending g ∈ G to e(G)|G : CG(g)| is a generalized character of G. It turns out that e(G) is strongly influenced by local data, but behaves irregularly for non-abelian simple groups. We interpret e(G) as an elementary divisor of a certain non-negative integral matrix related to the character table of G. Our methods applied to Brauer characters also answer a recent question of Navarro: The p-Brauer character table of G determines |G|p0.
AB - For a finite group G, we investigate the smallest positive integer e(G) such that the map sending g ∈ G to e(G)|G : CG(g)| is a generalized character of G. It turns out that e(G) is strongly influenced by local data, but behaves irregularly for non-abelian simple groups. We interpret e(G) as an elementary divisor of a certain non-negative integral matrix related to the character table of G. Our methods applied to Brauer characters also answer a recent question of Navarro: The p-Brauer character table of G determines |G|p0.
KW - Conjugation action
KW - Generalized character
UR - http://www.scopus.com/inward/record.url?scp=85112409705&partnerID=8YFLogxK
U2 - 10.5486/PMD.2021.9015
DO - 10.5486/PMD.2021.9015
M3 - Article
AN - SCOPUS:85112409705
VL - 99
SP - 243
EP - 260
JO - Publicationes mathematicae
JF - Publicationes mathematicae
SN - 0033-3883
IS - 1-2
M1 - 14
ER -