On finite point transitive affine planes with two orbits on \(\ell_{\infty}\)
type: Item
instance of: scholarly article
title: On finite point transitive affine planes with two orbits on \(\ell_{\infty}\)
zbMATH Open document ID: 0705.51002
author: Chihiro Suetake
published in: Osaka Journal of Mathematics
publication date: 1990-01-01T00:00:00Z
review text: The purpose of the paper is to study the following conjecture of Kallaher: Let \(\pi\) be a finite affine plane of order n with a collineation group G which is transitive on the affine points of \(\pi\). If G has two orbits on the line at infinity then one of the following statements holds: (I) The plane \(\pi\) is a transition plane and the group G contains the group of translations of \(\pi\), (II) The plane \(\pi\) is a dual translation plane, and the group G contains the group of dual translations of \(\pi\). It contains two theorems, first of them gives some sufficient conditions for a finite affine plane to be a translation plane, and the second theorem describes affine planes of order n with a collineation group which is transitive on affine points and which has two orbits of length 2 and n-1 on the line at infinity.
Mathematics Subject Classification ID: 51A40
zbMATH DE Number: 4157362
zbMATH Keywords: affine plane
zbMATH Keywords: collineation group
zbMATH Keywords: translation plane
reviewed by: J. Bureš
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4157362