A new family of 2-dimensional Laguerre planes that admit \(\mathrm{PSL}_2(\mathbb{R}) \times \mathbb{R}\) as a group of automorphisms (Q1623012)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: A new family of 2-dimensional Laguerre planes that admit \(\mathrm{PSL}_2(\mathbb{R}) \times \mathbb{R}\) as a group of automorphisms |
scientific article; zbMATH DE number 6983419
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A new family of 2-dimensional Laguerre planes that admit \(\mathrm{PSL}_2(\mathbb{R}) \times \mathbb{R}\) as a group of automorphisms |
scientific article; zbMATH DE number 6983419 |
Statements
A new family of 2-dimensional Laguerre planes that admit \(\mathrm{PSL}_2(\mathbb{R}) \times \mathbb{R}\) as a group of automorphisms (English)
0 references
22 November 2018
0 references
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.
0 references
Laguerre plane
0 references
topological incidence geometry
0 references
generalized quadrangle
0 references
0 references
0 references
