Realization of sporadic simple groups as Galois groups over cyclotomic fields.
type: Item
instance of: scholarly article
title: Realization of sporadic simple groups as Galois groups over cyclotomic fields.
zbMATH Open document ID: 0598.12006
DOI: 10.1016/0021-8693(86)90111-0
author: Gudrun Hoyden-Siedersleben
author: B. Heinrich Matzat
published in: Journal of Algebra
publication date: 1986-01-01T00:00:00Z
review text: The authors prove as a consequence of their Satz 1 the following interesting theorems. 1. The following 18 sporadic simple groups \(M_{11}\), \(M_{12}\), \(M_{22}\), \(J_ 1\), \(J_ 2\), \(HS\), \(Sz\), \(ON\), \(Co_ 3\), \(Co_ 2\), \(Co_ 1\), \(Fi_{22}\), \(Fi_{23}\), \(Fi'_{24}\), \(F_ 5\), \(F_ 3\), \(F_ 2\), \(F_ 1\) are realizable as Galois groups over the rational number field \({\mathbb Q}.\) 2. Let \({\mathbb Q}^{ab}={\mathbb Q}\) (all \(n\)th roots of unity for all \(n\)). Then all sporadic simple groups (except perhaps \(J_ 4)\) are realizable as Galois groups over \({\mathbb Q}^{ab}\).
Mathematics Subject Classification ID: 11R32
Mathematics Subject Classification ID: 12F12
Mathematics Subject Classification ID: 20D06
Mathematics Subject Classification ID: 20B25
Mathematics Subject Classification ID: 20F29
Mathematics Subject Classification ID: 11R18
zbMATH DE Number: 3963968
zbMATH Keywords: cyclotomic fields
zbMATH Keywords: sporadic simple groups as Galois groups over \({\mathbb Q}\)
zbMATH Keywords: inverse problem of Galois theory
describes a project that uses: CAS
MaRDI profile type: Publication
full work available at URL: 0021-8693(86)90111-0
OpenAlex ID: W2076580594
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description: scientific article; zbMATH DE number 3963968