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A FAMILY OF TWO-DIMENSIONAL LAGUERRE PLANES OF KLEINEWILLINGHÖFER TYPE II.A.2

Part of: Nonlinear incidence geometry Topological geometry

Published online by Cambridge University Press:  18 June 2018

GÜNTER F. STEINKE
GÜNTER F. STEINKE*
Affiliation:
School of Mathematics and Statistics, University of Canterbury, Private Bag 4800, Christchurch 8140, New Zealand email Gunter.Steinke@canterbury.ac.nz
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Abstract

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Kleinewillinghöfer classified Laguerre planes with respect to linearly transitive groups of central automorphisms. Polster and Steinke investigated two-dimensional Laguerre planes and their so-called Kleinewillinghöfer types. For some of the feasible types the existence question remained open. We provide examples of such planes of type II.A.2, which are based on certain two-dimensional Laguerre planes of translation type. With these models only one type, I.A.2, is left for which no two-dimensional Laguerre planes are known yet.

Keywords

Laguerre planeautomorphismKleinewillinghöfer type

MSC classification

Primary: 51H15: Topological nonlinear incidence structures
Secondary: 51B15: Laguerre geometries
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 105 , Issue 3 , December 2018 , pp. 366 - 379
Copyright
© 2018 Australian Mathematical Publishing Association Inc. 

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