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 -