On alternating and symmetric groups as Galois groups
type: Item
instance of: scholarly article
title: On alternating and symmetric groups as Galois groups
zbMATH Open document ID: 1067.12004
DOI: 10.1007/BF02771527
author: David Brink
published in: Israel Journal of Mathematics
publication date: 2004-10-15T00:00:00Z
review text: The main result of the paper under review states that the alternating group \(A_n,n\geq 3\) appears as Galois group over any Hilbertian fi eld of characteristic \(\neq 2\). In characteristic 2 the same statement holds for odd \(n\). The proof uses Newton polygons. It is further shown, that any quadratic extension of Hilbertian fields of characteristic different from 2 can be embedded in an \(S_n\)-extension.
Mathematics Subject Classification ID: 12F12
zbMATH DE Number: 2108113
zbMATH Keywords: Galois extension
zbMATH Keywords: Hilbertian fields
zbMATH Keywords: alternating group
zbMATH Keywords: symmetric group
zbMATH Keywords: Newton polygon
reviewed by: Martin Epkenhans
MaRDI profile type: Publication
cites work: Alternating group coverings of the affine line for characteristic two
cites work: Q3027108
cites work: Q5724382
cites work: Q4263461
cites work: Q4001587
cites work: Q4003835
cites work: Q3926778
description: scientific article; zbMATH DE number 2108113