4-dimensionale projektive Ebenen mit 3-dimensionaler Translationsgruppe
type: Item
instance of: scholarly article
title: 4-dimensionale projektive Ebenen mit 3-dimensionaler Translationsgruppe
zbMATH Open document ID: 0547.51012
DOI: 10.1007/BF00146829
author: Dieter Betten
published in: Geometriae Dedicata
publication date: 1984-01-01T00:00:00Z
review text: Let \({\mathbb{P}}\) be a topological projective plane whose point set is homeomorphic to that of the complex projective plane. The author makes the following assumptions: (1) There exists a line with respect to which \({\mathbb{P}}\) admits a 3-dimensional group G of translations, (2) G has an orbit invariant under the full collineation group. - He then classifies all such planes: They are ''sums'' of 2 ''halves'' of translation planes. The construction may be interpreted as a generalization of the Moulton construction for 2-dimensional planes.
reviewed by: Hansjoachim Groh
Mathematics Subject Classification ID: 51H10
zbMATH DE Number: 3872164
zbMATH Keywords: topological projective plane
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf00146829
OpenAlex ID: W2085298966
description: scientific article; zbMATH DE number 3872164