Vol. 17, No. 1, 2019

Download this article
Download this article For screen
For printing
Recent Issues
Volume 17, Issue 2
Volume 17, Issue 1
Volume 16, Issue 1
Volume 15, Issue 1
Volume 14, Issue 1
Volume 13, Issue 1
Volume 12, Issue 1
Volume 11, Issue 1
Volume 10, Issue 1
Volume 9, Issue 1
Volume 8, Issue 1
Volume 6+7, Issue 1
Volume 5, Issue 1
Volume 4, Issue 1
Volume 3, Issue 1
Volume 2, Issue 1
Volume 1, Issue 1
The Journal
About the Journal
Subscriptions
Editorial Board
Submission Guidelines
Submission Form
Ethics Statement
To Appear
Editorial Login
Contacts
ISSN (electronic): 2640-7345
ISSN (print): 2640-7337
Other MSP Journals
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