A new family of 2-dimensional Laguerre planes that admit \(\mathrm{PSL}_2(\mathbb{R}) \times \mathbb{R}\) as a group of automorphisms
type: Item
instance of: scholarly article
title: A new family of 2-dimensional Laguerre planes that admit \(\mathrm{PSL}_2(\mathbb{R}) \times \mathbb{R}\) as a group of automorphisms
zbMATH Open document ID: 1407.51006
author: Günter F. Steinke
published in: Innovations in Incidence Geometry
publication date: 2018-11-22T00:00:00Z
review text: The paper under review contributes to the investigation of 2-dimensional Laguerre planes with a 4-dimensional automorphism group. A new model of such planes is constructed and it is proved that they have \(\mathrm{PSL}_2(\mathbb{R}) \times \mathbb{R}\) as automorphism group. The planes belong to Kleinewillighöfer type 1.G.1 or VII.K.13 and in the first case they are not semiclassical. The author also investigates the associated compact 3-dimensional generalized quadrangles.
Mathematics Subject Classification ID: 51H15
Mathematics Subject Classification ID: 51B15
Mathematics Subject Classification ID: 51E12
zbMATH DE Number: 6983419
zbMATH Keywords: Laguerre plane
zbMATH Keywords: topological incidence geometry
zbMATH Keywords: generalized quadrangle
reviewed by: Dirk Keppens
MaRDI profile type: Publication
full work available at URL: iig.2019.17.53
OpenAlex ID: W2901625111
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DOI: 10.2140/IIG.2019.17.53
description: scientific article; zbMATH DE number 6983419