Some sporadic groups as Galois groups
type: Item
instance of: scholarly article
title: Some sporadic groups as Galois groups
zbMATH Open document ID: 0663.12013
published in: Rendiconti del Seminario Matematico della Università di Padova
publication date: 1988-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/108111
review text: In this paper it is proved that the sporadic simple groups \(He\), \(Fi_{22}\), \(J_4\), have GAR-realizations over \(\mathbb{Q}(T)\). According to Matzat's definition [\textit{B. H. Matzat}, Invent. Math. 80, 365-374 (1985; Zbl 0567.12015)], these groups are Galois groups of regular extensions of \(\mathbb{Q}(T)\) with two additional properties. As a consequence of this result and of previous work of Matzat and others, it is obtained that all sporadic simple groups have GAR-realizations over \(\mathbb{Q}^{ab}(T)\).
Mathematics Subject Classification ID: 11R32
Mathematics Subject Classification ID: 20D08
Mathematics Subject Classification ID: 20F29
zbMATH DE Number: 4083770
zbMATH Keywords: inverse problem of Galois theory
zbMATH Keywords: sporadic simple groups
zbMATH Keywords: GAR-realizations
author: Herbert Pahlings
reviewed by: Nuria Vila
describes a project that uses: CAS
MaRDI profile type: Publication
cites work: On extensions of the maximal cyclotomic field having a given classical Galois group.
cites work: Q3684278
cites work: Realization of sporadic simple groups as Galois groups over cyclotomic fields.
cites work: Realisierung endlicher Gruppen als Galoisgruppen. (Realization of finite groups as Galois groups)
cites work: Zum Einbettungsproblem der algebraischen Zahlentheorie mit nicht abelschem Kern
cites work: Rational rigidity and the sporadic groups
cites work: On the automorphism group of the group \(D_ 4(\)2)
cites work: Q3337625
cites work: Some finite groups which appear as Gal L/K, where \(K\subseteq {\mathbb{Q}}(\mu _ n)\)
Recommended article: Some sporadic groups as Galois groups. II
Recommended article: Q5287760
Recommended article: Q2969977
Recommended article: Realization of sporadic simple groups as Galois groups over cyclotomic fields.
Recommended article: Q4869726
Recommended article: A new characterization of sporadic simple groups
Recommended article: Sporadic simple groups which are Hurwitz
Recommended article: Q4209769
Recommended article: Q3804899
description: scientific article; zbMATH DE number 4083770