Some unitary groups as Galois groups over \({\mathbb{Q}}\)
type: Item
instance of: scholarly article
title: Some unitary groups as Galois groups over \({\mathbb{Q}}\)
zbMATH Open document ID: 0713.12004
DOI: 10.1016/0021-8693(90)90188-T
author: Gunter Malle
published in: Journal of Algebra
publication date: 1990-01-01T00:00:00Z
review text: The author shows that some finite unitary and special unitary groups are realizable as Galois groups over \({\mathbb{Q}}\). His method is based on an idea of Feit which starts from a finite simple group G with a nontrivial outer automorphism \(\rho\) which can be extended to the universal central extension \(\tilde G\) such that the extended group \(\tilde G:\)\(<\rho >\) has trivial center. Then the rationality criteria can be applied to \(\tilde G:\)\(<\rho >\) to obtain (perhaps) a Galois realization for \(\tilde G:\)\(<\rho >\). Finally an easy descent argument leads to a Galois realization for \(\tilde G.\) In this manner the special unitary group \(\tilde G:\)\(=SU_ 3(p)\), \(p>2\), which has a nontrivial center of order 3 for \(p\equiv -1 mod 3\) is examined in the paper under review.
Mathematics Subject Classification ID: 12F12
Mathematics Subject Classification ID: 20G40
Mathematics Subject Classification ID: 11R32
zbMATH DE Number: 4173147
zbMATH Keywords: finite unitary groups
zbMATH Keywords: Galois realization
reviewed by: Hans Opolka
MaRDI profile type: Publication
cites work: Q3611515
cites work: Q3682663
cites work: Q3812341
cites work: Exceptional groups of Lie type as Galois groups.
cites work: Konstruktive Galoistheorie. (Constructive Galois theory)
cites work: The Character Tables for SL(3, q), SU(3, q2), PSL(3, q), PSU(3, q2)
full work available at URL: 0021-8693(90)90188-t
OpenAlex ID: W2086784629
description: scientific article; zbMATH DE number 4173147