The symmetry axioms in Laguerre planes

2006/01/13 by Jarosław Kosiorek, Jaroslaw Kosiorek, Kosiorek, Jaroslaw +3
Mathematics · #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #Algebraic structures and combinatorial models #math.CO #math.MG #msc:51B20

paper · pdf · doi:10.48550/arxiv.math/0601321

9 p., 7 fig

arxiv created 2006/01/13 · arxiv updated 2009/12/01

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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