Infinite families of \(A_4\)-sextic polynomials
type: Item
instance of: scholarly article
zbMATH Open document ID: 1372.12001
DOI: 10.4153/CMB-2014-008-1
author: Joshua Ide
author: Lenny Jones
published in: Canadian Mathematical Bulletin
publication date: 2014-10-21T00:00:00Z
Mathematics Subject Classification ID: 12F10
Mathematics Subject Classification ID: 12F12
Mathematics Subject Classification ID: 11R32
Mathematics Subject Classification ID: 11R09
zbMATH DE Number: 6359644
zbMATH Keywords: Galois group
zbMATH Keywords: sextic polynomial
zbMATH Keywords: inverse Galois theory
MaRDI profile type: Publication
title: Infinite families of \(A_4\)-sextic polynomials
review text: The authors prove that if \(g(X) \in \mathbb{Z}[X]\) is a monic cubic polynomial such that \(f(X):=g(X^2)\) is irreducible over \(\mathbb{Q}\) and the discriminants of both \(f\) and \(g\) are squares in \(\mathbb{Z}\), then the Galois group of \(f\) is isomorphic to the alternating group \(A_4\). They use their test to obtain three infinite families of sextic polynomials irreducible over \(\mathbb{Q}\) with Galois group isomorphic to \(A_4\).
reviewed by: Teresa Crespo
description: scientific article; zbMATH DE number 6359644