## Abstract

The classical 2-dimensional Laguerre plane is obtained as the geometry of non-trivial plane sections of a cylinder in ℝ^{3} with a circle in ℝ^{2} as base. Points and lines in ℝ^{3} define subsets of the circle set of this geometry via the affine non-vertical planes that contain them. Furthermore, vertical lines and planes define partitions of the circle set via the points and affine non-vertical lines, respectively, contained in them. We investigate abstract counterparts of such sets of circles and partitions in arbitrary 2-dimensional Laguerre planes. We also prove a number of related results for generalized quadrangles associated with 2-dimensional Laguerre planes.

Original language | English |
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Pages (from-to) | 104-127 |

Number of pages | 24 |

Journal | Journal of the Australian Mathematical Society |

Volume | 62 |

Issue number | 1 |

Publication status | Published - Feb 1997 |

Externally published | Yes |

## Keywords

- Generalized quadrangle
- Laguerre plane
- Topological incidence geometry