Vol. 17, No. 1, 2019

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A new family of $2$-dimensional Laguerre planes that admit $\mathrm{PSL}_2(\mathbb R) \times\mathbb R$ as a group of automorphisms

Günter F. Steinke

Vol. 17 (2019), No. 1, 53–75
Abstract

We construct a new family of 2-dimensional Laguerre planes that differ from the classical real Laguerre plane only in the circles that meet a given circle in precisely two points. These planes share many properties with but are nonisomorphic to certain semiclassical Laguerre planes pasted along a circle in that they admit 4-dimensional groups of automorphisms that contain PSL2() and are of Kleinewillinghöfer type I.G.1.

Keywords
Laguerre plane, topological incidence geometry, generalized quadrangle
Mathematical Subject Classification 2010
Primary: 51H15
Secondary: 51B15
Milestones
Received: 2 November 2017
Revised: 20 November 2017
Accepted: 3 January 2018
Published: 19 November 2018
Authors
Günter F. Steinke
School of Mathematics and Statistics
University of Canterbury
Christchurch
New Zealand