Zur Archimedizität projektiver Ebenen über Cartesischen Gruppen
type: Item
instance of: scholarly article
title: Zur Archimedizität projektiver Ebenen über Cartesischen Gruppen
zbMATH Open document ID: 0592.51010
DOI: 10.1007/BF03322349
published in: Results in Mathematics
publication date: 1986-01-01T00:00:00Z
review text: Consider an ordered projective plane \({\mathcal P}\). For any figure \({\mathfrak e}=(K,w,L,u)\) with \(u,w\neq K\cap L=v\in uw\neq K,L,\) the Archimedean property (of repeated left addition with respect to \({\mathfrak e})\) mean that the projectivity \(\pi_{{\mathfrak e}}=(K,w,L,u,K)\) has unbounded orbits on \(K\setminus v\). If \({\mathcal P}\) is \({\mathfrak e}\)-Archimedean for each figure \({\mathfrak e}\) containing a given line W, then \({\mathcal P}\) is already fully Archimedean. Weaker conditions suffice in planes of Lenz type \(\neq I\).
Mathematics Subject Classification ID: 51G05
Mathematics Subject Classification ID: 06F15
zbMATH DE Number: 3951429
zbMATH Keywords: archimedean projective plane
zbMATH Keywords: archimedean Cartesian group
zbMATH Keywords: ordered projective plane
zbMATH Keywords: Archimedean property
zbMATH Keywords: planes of Lenz type
author: Franz B. Kalhoff
reviewed by: Helmut Salzmann
MaRDI profile type: Publication
cites work: Angeordnete projektive Ebenen
cites work: Über lokalarchimedische Anordnungen projektiver Ebenen. (On local- Archimedean orderings of projective planes)
cites work: Ordnungsfunktionen in nichtdesarguesschen projektiven Geometrien
cites work: Q4064611
cites work: Archimedisch angeordnete Ternärkörper
cites work: Zur Klassifikation topologischer Ebenen. I, II
description: scientific article; zbMATH DE number 3951429