Vol. 17, No. 1, 2019
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Generalized quadrangles, Laguerre planes and shift planes of odd order

Günter F. Steinke and Markus Stroppel
Vol. 17 (2019), No. 1, 47–52
DOI: 10.2140/iig.2019.17.47
Abstract

We characterize the Miquelian Laguerre planes, and thus the classical orthogonal generalized quadrangles Q(4,q), of odd order q by the existence of shift groups in affine derivations.

Keywords
generalized quadrangle, orthogonal generalized quadrangle, antiregular translation generalized quadrangle, Laguerre plane, Miquelian Laguerre plane, translation plane, shift plane, shift group
Mathematical Subject Classification 2010
Primary: 51B15, 51E12, 51E15
Secondary: 05B25, 51E25
Milestones
Received: 11 October 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
Markus Stroppel
LExMath, Fakultät für Mathematik und Physik
Universität Stuttgart
Stuttgart
Germany