The maximal subgroups of the Steinberg triality groups \(3D_ 4(q)\) and their automorphism groups
type: Item
instance of: scholarly article
title: The maximal subgroups of the Steinberg triality groups \(3D_ 4(q)\) and their automorphism groups
zbMATH Open document ID: 0642.20013
DOI: 10.1016/0021-8693(88)90290-6
published in: Journal of Algebra
publication date: 1988-01-01T00:00:00Z
review text: The author determines the maximal subgroups of the finite Steinberg groups \(3D_ 4(q)\), and of their automorphism groups. This involves embedding \(3D_ 4(q)\) in \(O\) \(+_ 8(q\) 3) and using the associated geometry of triality to investigate the embeddings of maximal subgroups in \(3D_ 4(q)\). Much use is made of the author's earlier paper on the maximal subgroups of \(O\) \(+_ 8(q)\) [J. Algebra 110, 173-242 (1987; Zbl 0623.20031)], which is also used in his determination of the maximal subgroups of \(G_ 2(q)\) for q odd, and the Ree groups \(2G_ 2(q)\) [ibid. 117, No.1, 30-71 (1988)]. As is usual in this area, this work relies on the classification of finite simple groups.
reviewed by: Robert A. Wilson
Mathematics Subject Classification ID: 20D06
Mathematics Subject Classification ID: 20D30
Mathematics Subject Classification ID: 20E28
zbMATH DE Number: 4045996
zbMATH Keywords: maximal subgroups
zbMATH Keywords: finite Steinberg groups
zbMATH Keywords: automorphism groups
zbMATH Keywords: triality
zbMATH Keywords: Ree groups
author: Peter B. Kleidman
MaRDI profile type: Publication
full work available at URL: 0021-8693(88)90290-6
OpenAlex ID: W2061974292
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description: scientific article; zbMATH DE number 4045996