Finite doubly transitive affine planes
type: Item
instance of: scholarly article
title: Finite doubly transitive affine planes
zbMATH Open document ID: 0915.51002
author: Vikram Jha
author: Norman L. Johnson
published in: Journal of Combinatorial Theory. Series A
publication date: 1999-07-05T00:00:00Z
review text: The authors classify all finite affine planes with a doubly transitive automorphism group (on the points). First they remark that such a plane is always a translation plane and that the ``solvable case'' has been treated by \textit{D. A. Foulser} already [Math. Z. 86, 191-204 (1964; Zbl 0144.01803)]. Then they apply a result of Hering, who classified non-solvable linear groups acting transitively on the non-zero vectors of a finite vector space. A case-by-case study finishes the classification. Besides the Desarguesian affine planes, one finds the Hall plane of order 9 and the Hering plane of order 27.
Mathematics Subject Classification ID: 51E15
zbMATH DE Number: 1212921
zbMATH Keywords: finite affine planes
zbMATH Keywords: doubly transitive automorphism
reviewed by: Hendrik Van Maldeghem
MaRDI profile type: Publication
full work available at URL: jcta.1997.2862
OpenAlex ID: W1984109300
cites work: The uniqueness of Hering's translation plane of order 27
cites work: Solvable flag transitive affine groups
cites work: Transitive linear groups and linear groups which contain irreducible subgroups of prime order
cites work: The translation planes admitting a nonsolvable doubly transitive line-sized orbit
cites work: Q3891315
cites work: On projective and affine planes with transitive collineation groups
cites work: On finite affine line transitive planes
DOI: 10.1006/JCTA.1997.2862
description: scientific article; zbMATH DE number 1212921