Equations in characteristic 3 with Mathieu groups as their Galois groups
type: Item
instance of: scholarly article
title: Equations in characteristic 3 with Mathieu groups as their Galois groups
zbMATH Open document ID: 0847.12002
DOI: 10.1007/BF01264934
author: Ikkwon Yie
published in: Geometriae Dedicata
publication date: 1996-10-14T00:00:00Z
review text: Im Anschluß an eine bekannte Vermutung von Abhyankar betreffend unverzweigte Überlagerungen der affinen Geraden über einem Körper von Primzahlcharakteristik werden für einen beliebigen Körper \(k\) der Charakteristik 3 die folgenden Polynome betrachtet: \[ F_a(X,Y) = Y^{12} + aY^6 + XY^3 + Y + 1 \in k[X,Y] \quad \text{und} \quad \widetilde F_a = F_a (X,Y^2), \] wobei \(a\) ein Element in \(k\) ist. U. a. wird bewiesen, daß die Zerfällungskörper von \(F_a\) und \(\widetilde F_a\) über \(k(X)\) an allen endlichen Stellen unverzweigt sind. Wenn \(a = \pm 1\) ist, ist die Galoissche Gruppe von \(F_a\), bzw. \(\widetilde F_a\) über \(k(X)\) die Mathieugruppe \(M_{12}\), bzw. deren universelle Überlagerungsgruppe \(\widetilde M_{12}\).
Mathematics Subject Classification ID: 12F12
Mathematics Subject Classification ID: 14H30
Mathematics Subject Classification ID: 12F10
Mathematics Subject Classification ID: 20E22
Mathematics Subject Classification ID: 20D06
Mathematics Subject Classification ID: 12E05
zbMATH DE Number: 806279
zbMATH Keywords: Abhyankar conjecture
zbMATH Keywords: affine line over a field of prime characteristic
zbMATH Keywords: Galois group
zbMATH Keywords: Mathieu group
zbMATH Keywords: universal covering group
zbMATH Keywords: splitting field
reviewed by: Christian U. Jensen
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01264934
OpenAlex ID: W1967889775
description: scientific article; zbMATH DE number 806279