Flag-transitive finite simple groups
type: Item
instance of: scholarly article
title: Flag-transitive finite simple groups
zbMATH Open document ID: 0582.51005
DOI: 10.1007/BF01189977
author: Anne Delandtsheer
published in: Archiv der Mathematik
publication date: 1986-01-01T00:00:00Z
review text: This paper is part of a programme aiming at the classification of all pairs (S,G) where S is a finite linear space (or a 2-(v,k,1) design) and G is a flag-transitive automorphism group of S (flag means incident point-line pair). As shown in a forthcoming paper by Buekenhout, Delandtsheer and Doyen, the group G is necessarily either of affine or of simple type. We determine here all pairs (S,G) where G is one of the simple groups Sz(q), PSL(2,q), PSL(3,q) and PSU(3,q). The resulting linear spaces are the Desarguesian projective planes, the hermitian unitals and those derived from a projective plane P of even order provided with a complete conic C by calling points the lines of P disjoint from C and lines the points of P outside C, with the natural incidence.
Mathematics Subject Classification ID: 51E10
Mathematics Subject Classification ID: 20B25
zbMATH DE Number: 3931890
zbMATH Keywords: block design
zbMATH Keywords: Steiner system
zbMATH Keywords: linear space
zbMATH Keywords: flag-transitive automorphism group
zbMATH Keywords: Desarguesian projective planes
zbMATH Keywords: hermitian unitals
zbMATH Keywords: complete conic
MaRDI profile type: Publication
cites work: The Nonexistence of Certain Finite Projective Planes
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cites work: Geometric ABA-groups
cites work: Endliche Gruppen I
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full work available at URL: https://doi.org/10.1007/bf01189977
OpenAlex ID: W2011762408
description: scientific article; zbMATH DE number 3931890