A new family of 2-dimensional Laguerre planes that admit \(\mathrm{PSL}_2(\mathbb{R}) \times \mathbb{R}\) as a group of automorphisms
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.
scientific article; zbMATH DE number 6983419