Finite projective planes admitting a projective linear group \(\operatorname{PSL}(2, q)\)
type: Item
instance of: scholarly article
title: Finite projective planes admitting a projective linear group \(\operatorname{PSL}(2, q)\)
zbMATH Open document ID: 1088.05016
author: Jinglei Li
author: Weijun Liu
published in: Linear Algebra and its Applications
publication date: 2006-03-16T00:00:00Z
review text: A linear space \(\mathcal S\) is a set \(\mathcal P\) of points, together with a set \(\mathcal L\) of distinguished subsets called lines such that any two points lie on exactly one line. The groups of automorphisms of linear spaces which are line-transitive (and so, point-transitive by Block's theorem [\textit{R. E. Block}, Math. Z. 96, 33--49 (1967; Zbl 0163.42304)]) have greatly been considered by a large number of people. The present paper continues in that tradition and the following result is proved. Theorem. Let \(G\leq\) Aut\((\mathcal S)\), where \(\mathcal S\) is a projective plane, and PSL\((2, q)\leq G\leq \text{P}\Gamma \text{L}(2, q)\) with \(q > 3\). If \(G\) acts point-transitively on \(\mathcal S\), then \(q = 7\) and \(\mathcal S\) is of order \(2\).
reviewed by: V. Napolitano
Mathematics Subject Classification ID: 05B05
Mathematics Subject Classification ID: 20B25
zbMATH DE Number: 5012993
zbMATH Keywords: point-transitive
zbMATH Keywords: involution
MaRDI profile type: Publication
full work available at URL: j.laa.2005.08.026
OpenAlex ID: W1996766531
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DOI: 10.1016/J.LAA.2005.08.026
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description: scientific article; zbMATH DE number 5012993