Quadratic extensions of flag-transitive planes
type: Item
instance of: scholarly article
title: Quadratic extensions of flag-transitive planes
zbMATH Open document ID: 0955.51002
author: Yutaka Hiramine
author: Norman L. Johnson
author: Vikram Jha
published in: European Journal of Combinatorics
publication date: 2001-02-16T00:00:00Z
review text: A finite affine plane \(\pi\) of order \(q^2\) which has a subplane \(\pi_0\) of order \(q\) is called a quadratic extension of a flag-transitive plane if it admits a collineation group \(G\) which leaves \(\pi_0\) invariant, acts transitively on the flags of \(\pi_0\), and acts transitively on the lines of \(\pi\) intersecting \(\pi_0\) in precisely one affine point. The authors prove that the only finite translation planes which are quadratic extensions of flag-transitive planes are the Desarguesian planes, the Hall planes, and the derived likeable Walker plane of order 25.
reviewed by: Norbert Knarr
Mathematics Subject Classification ID: 51A40
Mathematics Subject Classification ID: 51E15
zbMATH DE Number: 1417656
MaRDI profile type: Publication
full work available at URL: eujc.1999.0333
OpenAlex ID: W1969204203
cites work: Linear spaces with flag-transitive automorphism groups
cites work: Q3684278
cites work: Minimal degree for a permutation representation of a classical group
cites work: The Flag-Transitive Collineation Groups of the Finite Desarguesian Affine Planes
cites work: Solvable flag transitive affine groups
cites work: Subplanes of Partial Spreads in Translation Planes
cites work: Baer p-elements in translation planes
cites work: Solvable, flag-transitive, rank 3 collineation groups
cites work: The translation planes of order \(q_ 2\) that admit SL(2,q) as a collineation group. II: Odd order
cites work: The translation planes of order \(q_ 2\) that admit SL(2,q) as a collineation group. I: Even order
cites work: Q5577154
cites work: On shears of translation planes
cites work: On finite line transitive affine planes
cites work: Transitive linear groups and linear groups which contain irreducible subgroups of prime order
cites work: Q3105730
cites work: On transitive automorphism groups of finite quasifields
cites work: Translation planes of order \(q^ 2\) that admit \(q+1\) elations
cites work: Regular parallelisms from translation planes
cites work: Q3739794
cites work: Q4734377
cites work: Q3490540
cites work: Translation planes of large dimension admitting nonsolvable groups
cites work: Bol quasifields and generalized Andre systems
cites work: Q3891315
cites work: Nets with critical deficiency
cites work: Linear transformations and collineations of translation planes
cites work: Elations in finite translation planes of characteristic 3
cites work: Regular packings of \(PG(3,q)\)
cites work: The cyclic parallelism of PG(3,5)
DOI: 10.1006/EUJC.1999.0333
description: scientific article; zbMATH DE number 1417656