The reciprocal character of the conjugation action

verfasst von

Benjamin Sambale

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.

Organisationseinheit(en)

Institut für Algebra, Zahlentheorie und Diskrete Mathematik

Typ

Artikel

Journal

Publicationes mathematicae

Band

99

Seiten

243-260

Anzahl der Seiten

18

ISSN

0033-3883

Publikationsdatum

2021

Publikationsstatus

Veröffentlicht

Peer-reviewed

Ja

ASJC Scopus Sachgebiete

Mathematik (insg.)

Elektronische Version(en)

https://arxiv.org/abs/2003.06150 (Zugang: Offen)
https://doi.org/10.5486/PMD.2021.9015 (Zugang: Geschlossen)