Maximal subgroups of finite symplectic groups stabilizing spreads of lines.
type: Item
instance of: scholarly article
title: Maximal subgroups of finite symplectic groups stabilizing spreads of lines.
zbMATH Open document ID: 1041.20033
DOI: 10.1016/S0021-8693(02)00639-7
author: Oliver King
author: Antonio Cossidente
published in: Journal of Algebra
publication date: 2003-02-12T00:00:00Z
review text: The authors describe the embedding \(\iota\colon\text{U}_n(q^2)\to\text{Sp}_{2n}(q)\) and a certain line spread of \(\text{PG}(2n-1,q)\). Let \(G\) be the group \(\iota(\langle U_n(q^2),\tau\sigma\rangle)\), where \(\sigma\) is the Frobenius automorphism \(\Theta\to\Theta^q\) for \(\Theta\) in \(\text{GF}(q^2)\), and \(\tau\) is a suitable mapping in \(\text{GU}_n(q^2)\). The authors show that \(G\) is the stabilizer of a certain line spread and that it is maximal in the symplectic group \(\text{Sp}_{2n}(q)\), except when \(n=2\) and \(q=3\). Similar results were obtained by \textit{P. Kleidman} and \textit{M. Liebeck} [The subgroup structure of the finite classical groups (Lond. Math. Soc. Lect. Note Ser., Vol. 129, Cambridge University Press, Cambridge), (1990; Zbl 0697.20004)]. The proof given here is geometrical. It supplements research done by R. H. Dye in several papers.
reviewed by: Erich W. Ellers
Mathematics Subject Classification ID: 20G40
Mathematics Subject Classification ID: 14L35
Mathematics Subject Classification ID: 20E28
zbMATH DE Number: 1868098
zbMATH Keywords: symplectic groups
zbMATH Keywords: unitary groups
zbMATH Keywords: maximal subgroups
zbMATH Keywords: spreads of lines
MaRDI profile type: Publication
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full work available at URL: s0021-8693(02)00639-7
OpenAlex ID: W1979578282
description: scientific article; zbMATH DE number 1868098