Zum Einbettungsproblem der algebraischen Zahlentheorie mit nicht abelschem Kern
type: Item
instance of: scholarly article
title: Zum Einbettungsproblem der algebraischen Zahlentheorie mit nicht abelschem Kern
zbMATH Open document ID: 0567.12015
DOI: 10.1007/BF01388611
author: B. Heinrich Matzat
published in: Inventiones Mathematicae
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/143235
review text: The author investigates the following timely problem: Which composite finite groups can be the Galois group over a Hilbert field, i.e., a field where Hilbert's irreducibility condition is fulfilled. He proves that this depends on a special case of realizability of the factors as Galois groups over the field of rational functions (Satz 1) over the given field. To complete the result he proves in two special cases which sporadic groups have such a representation.
Mathematics Subject Classification ID: 12F10
Mathematics Subject Classification ID: 20F29
Mathematics Subject Classification ID: 12F20
Mathematics Subject Classification ID: 11S15
zbMATH DE Number: 3904712
zbMATH Keywords: embedding problem of algebraic number theory
zbMATH Keywords: non-abelian kernel
zbMATH Keywords: Hilbert irreducibility theorem
zbMATH Keywords: inverse Galois problem
zbMATH Keywords: composite finite groups
zbMATH Keywords: Hilbert field
zbMATH Keywords: rational functions
zbMATH Keywords: sporadic groups
reviewed by: Ervin Fried
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3904712