The Galois groups of the polynomials \(x^ n+ax^ s+b\). II
type: Item
instance of: scholarly article
title: The Galois groups of the polynomials \(x^ n+ax^ s+b\). II
zbMATH Open document ID: 0615.12012
author: Hiroyuki Osada
published in: Tôhoku Mathematical Journal. Second Series
publication date: 1987-01-01T00:00:00Z
review text: [For part I, see J. Number Theory 25, 230-238 (1987; Zbl 0608.12010).] This paper gives conditions under which the Galois group of a polynomial \(x^ n+ax^ s+b\) over the rational number field \({\mathbb{Q}}\) is isomorphic to the symmetric group \(S_ n\). Further, this paper gives a criterion for the Galois group of a polynomial over \({\mathbb{Q}}\) to be isomorphic to \(S_ n\) or to \(A_ n\). The author also constructs infinitely many polynomials with the Galois groups \(A_ 4\), \(A_ 5\) and \(A_ 7\).
Mathematics Subject Classification ID: 11R32
Mathematics Subject Classification ID: 20F29
Mathematics Subject Classification ID: 11R09
zbMATH DE Number: 3995826
zbMATH Keywords: prescribed Galois group
zbMATH Keywords: Galois group of polynomial
zbMATH Keywords: symmetric group
zbMATH Keywords: Galois group isomorphic to \(S_ n\)
zbMATH Keywords: Galois group isomorphic to \(A_ n\)
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1178228289
OpenAlex ID: W2046083530
cites work: The Galois groups of the polynomials \(X^ n+aX\ell +b\)
cites work: Q3320485
cites work: Q5512231
DOI: 10.2748/TMJ/1178228289
description: scientific article; zbMATH DE number 3995826