Flag-transitive and almost simple orbits in finite projective planes
type: Item
instance of: scholarly article
title: Flag-transitive and almost simple orbits in finite projective planes
zbMATH Open document ID: 1202.51007
author: Alessandro Montinaro
published in: Innovations in Incidence Geometry
publication date: 2010-09-20T00:00:00Z
review text: Let \(\Pi\) be a projective plane of order \(n\) admitting a collineation group \(G\) which acts doubly transitively (flag transitively) on a point-subset \(\mathcal O\) of size \(v\). Then \(\mathcal O\) is either (i) a non-trivial 2-\((v, k, 1)\) design, (ii) an arc, or (iii) a subset of a line. The paper focuses on the case (i) under the assumptions that \(G\) induces a flag-transitive and almost simple automorphism group on \(\mathcal O\) and \(n \leq \sum ({\mathcal O}) = b + v + r + k\), where \(b\) denotes the number of blocks of \(\mathcal O\) and \(r\) the number of blocks of \(\mathcal O\) incident with any given point of \(\mathcal O\). The author arrives (Theorem 1.1) at ten distinct cases when \(G\) acts faithfully on \(\mathcal O\) and two cases when this action is non-faithful, either ``regime'' being characterized by one open case. Reviewer's remark: In case (2a) of Theorem 1.1 there is an obvious misprint: ``75'' should read ``57''.
reviewed by: Metod Saniga
Mathematics Subject Classification ID: 51E15
Mathematics Subject Classification ID: 20B25
zbMATH DE Number: 5788607
zbMATH Keywords: projective plane
zbMATH Keywords: collineation group
zbMATH Keywords: orbit
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5788607