Accessible characters are monomial
type: Item
instance of: scholarly article
title: Accessible characters are monomial
zbMATH Open document ID: 0651.20011
DOI: 10.1016/0021-8693(88)90253-0
author: Everett C. Dade
published in: Journal of Algebra
publication date: 1988-01-01T00:00:00Z
review text: The following theorem is proved: Let G be a solvable finite group, \(N\trianglelefteq G\), \(\chi\in Irr(G)\), \(\chi =\sum_{i}z_ i\lambda_ i^{G}\), \((z_ i\in {\mathbb{Z}})\), the \(\lambda_ i^{G}\) induced from linear characters \(\lambda_ i\) of subnormal subgroups of N. Then \(\chi =\nu^{G}\) is induced from a linear character \(\nu\) of some subnormal subgroup of N. This theorem shows that for such non-principal \(\chi\) Artin's conjecture about holomorphic L-series is true. For these \(\chi\), written in the form \(\chi =\sum_{i}z_ i\lambda_ i^{G}\), \((z_ i\in {\mathbb{Z}})\), this was shown by J. Arthur and L. Clozel by means of some considerable effort [see: \textit{L. Clozel}, Base change for GL(n), in Proc. Int. Congr. Math. 1986 (1987)].
reviewed by: Robert W. van der Waall
Mathematics Subject Classification ID: 20C15
Mathematics Subject Classification ID: 11F70
zbMATH DE Number: 4061483
zbMATH Keywords: monomial characters
zbMATH Keywords: solvable finite group
zbMATH Keywords: linear characters
zbMATH Keywords: subnormal subgroups
zbMATH Keywords: Artin's conjecture
zbMATH Keywords: holomorphic L-series
MaRDI profile type: Publication
full work available at URL: 0021-8693(88)90253-0
OpenAlex ID: W2022047337
cites work: Q3818502
cites work: Endliche Gruppen I
description: scientific article; zbMATH DE number 4061483