Realisierbarkeit von Darstellungen endlicher Gruppen in Einheitswurzelkörpern. (Realizability of representations of finite groups in cyclotomic fields)
type: Item
instance of: scholarly article
title: Realisierbarkeit von Darstellungen endlicher Gruppen in Einheitswurzelkörpern. (Realizability of representations of finite groups in cyclotomic fields)
zbMATH Open document ID: 0695.20003
DOI: 10.1007/BF02568421
author: Frank Jonas
published in: Manuscripta Mathematica
publication date: 1990-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/155488
review text: The content of this paper is described in the author's summary: ``Let D: \(G\to GL(n,{\mathbb{C}})\) be an irreducible linear representation of a finite group G with the character \(\chi\). If D is realizable in \({\mathbb{Q}}(\xi_ m)\) and \({\mathbb{Q}}(\xi_{m'})\) we give a condition for the realizability of D in \({\mathbb{Q}}(\xi_{(m,m')})\). If the degree n is a prime \(\neq 2\), we show that D is realizable in \({\mathbb{Q}}(\xi_ f)\), where f is the conductor of the abelian extension \({\mathbb{Q}}(\chi)/{\mathbb{Q}}.''\) The problem was motivated by certain questions in the theory of Galois representations.
reviewed by: Hans Opolka
Mathematics Subject Classification ID: 20C15
Mathematics Subject Classification ID: 11R32
zbMATH DE Number: 4138019
zbMATH Keywords: rationality questions
zbMATH Keywords: irreducible linear representation
zbMATH Keywords: finite group
zbMATH Keywords: character
zbMATH Keywords: realizability
zbMATH Keywords: conductor
zbMATH Keywords: Galois representations
MaRDI profile type: Publication
cites work: Endliche Gruppen I
cites work: The Schur subgroup of the Brauer group
OpenAlex ID: W2094032109
description: scientific article; zbMATH DE number 4138019