Finite flag-transitive projective planes: A survey and some remarks
type: Item
instance of: scholarly article
title: Finite flag-transitive projective planes: A survey and some remarks
zbMATH Open document ID: 1026.51005
DOI: 10.1016/S0012-365X(02)00823-3
author: Koen Thas
published in: Discrete Mathematics
publication date: 2003-06-09T00:00:00Z
review text: The main problem which is discussed in this paper is the characterization of finite Desarguesian planes by certain transitivity properties. Most of the paper provides a detailed outline on the subject of flag-transitive projective planes. In particular considerable results obtained on this topic by Ostrom, Wagner, Ott, McLaughlim, Higman, Roth, Feit, Fink and others are reported. These results are split up in two categories: those established before \(1980\) (obtained essentially by geometrical methods) and those established after \(1980\) (obtained by using group theory and pure algebra). In the last part of the paper, the author considers polarities of projective planes admitting an abelian Singer group. Some new results in case the full automorphism group of the plane acts semiregularly on the flags are obtained.
reviewed by: Gloria Rinaldi
Mathematics Subject Classification ID: 51E15
zbMATH DE Number: 1924781
zbMATH Keywords: characterization of finite Desarguesian planes
zbMATH Keywords: transitivity properties
zbMATH Keywords: flag-transitive projective planes
zbMATH Keywords: polarities
MaRDI profile type: Publication
cites work: Q4718791
cites work: Q5848209
cites work: Q5545191
cites work: Q4882944
cites work: Finite Projective Planes and a Question about Primes
cites work: Q3314470
cites work: Flag-transitive projective planes
cites work: Q4243065
cites work: Cyclic projective planes
cites work: Geometric ABA-groups
cites work: Q5683869
cites work: On the geometry of planar difference sets
cites work: Primitive permutation groups of odd degree, and an application to finite projective planes
cites work: Q4007802
cites work: On projective and affine planes with transitive collineation groups
cites work: Fahnentransitive Ebenen gerader Ordnung
cites work: Fahnentransitive Ebenen ungerader Ordnung
cites work: Q4309517
cites work: Flag-Transitive Planes of Even Order
cites work: On involutions of projective planes
cites work: On finite affine line transitive planes
description: scientific article; zbMATH DE number 1924781