Innovations in Incidence Geometry — Algebraic, Topological and Combinatorial

Generalized quadrangles, Laguerre planes and shift planes of odd order

Günter F. Steinke and Markus Stroppel

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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.

Article information

Innov. Incidence Geom. Algebr. Topol. Comb., Volume 17, Number 1 (2019), 47-52.

Received: 11 October 2017
Revised: 20 November 2017
Accepted: 3 January 2018
First available in Project Euclid: 26 February 2019

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 51B15: Laguerre geometries 51E12: Generalized quadrangles, generalized polygons 51E15: Affine and projective planes
Secondary: 05B25: Finite geometries [See also 51D20, 51Exx] 51E25: Other finite nonlinear geometries

generalized quadrangle orthogonal generalized quadrangle antiregular translation generalized quadrangle Laguerre plane Miquelian Laguerre plane translation plane shift plane shift group


Steinke, Günter F.; Stroppel, Markus. Generalized quadrangles, Laguerre planes and shift planes of odd order. Innov. Incidence Geom. Algebr. Topol. Comb. 17 (2019), no. 1, 47--52. doi:10.2140/iig.2019.17.47.

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