Some properties of the absolute Galois group of a Hilbertian field
type: Item
instance of: scholarly article
title: Some properties of the absolute Galois group of a Hilbertian field
zbMATH Open document ID: 0613.12017
DOI: 10.1007/BF02801993
author: Zoé Chatzidakis
published in: Israel Journal of Mathematics
publication date: 1986-01-01T00:00:00Z
review text: The author proves the following results on the structure of absolute Galois groups G of Hilbertian fields: If the field is countable, then for almost all \(\sigma_ 1,...,\sigma_ e\) in \(G^ e\) (with respect to Haar measure) the group \(<\sigma >\) generated by \(\sigma_ 1,...,\sigma_ e\) is its own normalizer in G with trivial centralizer in case \(e>1.\) Suppose \(\tau_ 1,...,\tau_ f\) are given in \(G^ f\), then for almost all \(\sigma_ 1,...,\sigma_ e\) in the sense above \(<\tau >\cap <\sigma >=1\) holds.
Mathematics Subject Classification ID: 12F99
Mathematics Subject Classification ID: 12F10
Mathematics Subject Classification ID: 12F20
Mathematics Subject Classification ID: 20B27
zbMATH DE Number: 3991635
zbMATH Keywords: absolute Galois groups
zbMATH Keywords: Hilbertian fields
zbMATH Keywords: Haar measure
MaRDI profile type: Publication
cites work: Q4830003
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full work available at URL: https://doi.org/10.1007/bf02801993
OpenAlex ID: W2324251089
description: scientific article; zbMATH DE number 3991635