Some sporadic groups as Galois groups. II
type: Item
instance of: scholarly article
title: Some sporadic groups as Galois groups. II
zbMATH Open document ID: 0714.11075
published in: Rendiconti del Seminario Matematico della Università di Padova
publication date: 1989-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/108156
review text: [For part I, cf. Rend. Semin. Mat. Univ. Padova 79, 97-107 (1988; Zbl 0663.12013)]. It is proved that the sporadic simple groups \(J_ 3\), McL, Ru and Ly as well as their automorphism groups are Galois groups over \({\mathbb{Q}}(T)\). The author shows that these groups have a GAR-realization over \({\mathbb{Q}}(T)\), using \textit{B. H. Matzat}'s criterion [Invent. Math. 80, 365-374 (1985; Zbl 0567.12015)]. Summarizing previous results of Hoyden- Siedersleben, Hunt, Matzat and the author it is obtained that all sporadic simple groups, except the Mathieu group \(M_{23}\), are Galois groups of regular extensions of \({\mathbb{Q}}(T)\).
Mathematics Subject Classification ID: 11R32
Mathematics Subject Classification ID: 12F12
Mathematics Subject Classification ID: 20D08
Mathematics Subject Classification ID: 20F29
Mathematics Subject Classification ID: 11R58
zbMATH DE Number: 4175076
zbMATH Keywords: inverse Galois problem
zbMATH Keywords: sporadic simple groups
zbMATH Keywords: Galois groups
zbMATH Keywords: regular extensions
author: Herbert Pahlings
reviewed by: Nuria Vila
describes a project that uses: CAS
MaRDI profile type: Publication
cites work: Q3684278
cites work: Realization of sporadic simple groups as Galois groups over cyclotomic fields.
cites work: Rational rigidity and the sporadic groups
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: Konstruktive Galoistheorie. (Constructive Galois theory)
cites work: Q3337625
cites work: Some sporadic groups as Galois groups
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
Recommended article: Errata corrige: Some sporadic groups as Galois groups. II
Recommended article: A Conjecture of Frobenius and the Sporadic Simple Groups, II
Recommended article: Q2969977
Recommended article: Q5287760
Recommended article: Realization of sporadic simple groups as Galois groups over cyclotomic fields.
Recommended article: Q3428801
Recommended article: On 2-Groups as Galois Groups
Recommended article: Q4209769
Recommended article: Q4869726
description: scientific article; zbMATH DE number 4175076