Translations in affine Klingenberg spaces
type: Item
instance of: scholarly article
title: Translations in affine Klingenberg spaces
zbMATH Open document ID: 1230.51004
published in: Journal of Geometry
publication date: 2011-10-25T00:00:00Z
review text: The authors prove the Little Theorem of Desargues in affine Klingenberg spaces \(A\) of dimension at least 3. This allows to construct many translations. In fact, by Theorems 5.10 and 5.11 the translations of \(A\) form an abelian group which is sharply transitive on points. Moreover, it is shown that several different definitions of translations are equivalent if any two points lie on at least one line.
reviewed by: Theo Grundhöfer
Mathematics Subject Classification ID: 51C05
Mathematics Subject Classification ID: 51A30
Mathematics Subject Classification ID: 51D15
zbMATH DE Number: 5963293
zbMATH Keywords: affine Klingenberg space
zbMATH Keywords: translation
zbMATH Keywords: dilatation
author: T. Bisztriczky
author: J. W. Michael Lorimer
MaRDI profile type: Publication
full work available at URL: s00022-011-0067-1
OpenAlex ID: W1985873720
cites work: Q4039891
cites work: Q3662198
cites work: An affine characterization of Moufang projective Klingenberg planes
cites work: Q4505257
cites work: On hyperplanes and free subspaces of affine Klingenberg spaces
cites work: Subspace operations in affine Klingenberg spaces
cites work: Homomorphisms of affine spaces
cites work: Verallgemeinerte Andre-Ebenen mit Epimorphismen auf Hjelmslev-Ebenen
cites work: Projektive Geometrien mit Homomorphismus
cites work: Affine geometry over free unitary modules
cites work: On classifying affine Barbilian spaces
cites work: Rings of stable rank 2 are Barbilian rings
cites work: Desarguesian affine Hjelmslev planes.
cites work: Projektive Hjelmslevräume.
cites work: Affine Hjelmslev-Ebenen mit transitiver Translationsgruppe
cites work: Desarguessche affine Ebenen mit Homomorphismus
cites work: Q3906703
cites work: Q4763229
cites work: Q5543983
DOI: 10.1007/S00022-011-0067-1
description: scientific article; zbMATH DE number 5963293