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The Symmetry Axioms in Laguerre Planes

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Abstract

We introduce two axioms in Laguerre geometry and prove that they provide a characterization of miquelian planes over fields of the characteristic different from 2. They allow to describe an involutory automorphism that sheds some new light on a Laguerre inversion as well as on a symmetry with respect to a pair of generators.

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Authors and Affiliations

  1. Department of Mathematics and Informatics, UWM Olsztyn Żolnierska 14, 10-561, Olsztyn, Poland

    Jaroslaw Kosiorek & Andrzej Matraś

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  1. Jaroslaw Kosiorek
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  2. Andrzej Matraś
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Correspondence to Jaroslaw Kosiorek.

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Kosiorek, J., Matraś, A. The Symmetry Axioms in Laguerre Planes. Results. Math. 48, 237–245 (2005). https://doi.org/10.1007/BF03323367

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  • DOI: https://doi.org/10.1007/BF03323367

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