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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