The reciprocal character of the conjugation action

authored by

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.

Organisation(s)

Institute of Algebra, Number Theory and Discrete Mathematics

Type

Article

Journal

Publicationes mathematicae

Volume

99

Pages

243-260

No. of pages

18

ISSN

0033-3883

Publication date

2021

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

Mathematics(all)

Electronic version(s)

https://arxiv.org/abs/2003.06150 (Access: Open)
https://doi.org/10.5486/PMD.2021.9015 (Access: Closed)