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Some chain geometries determined by transformation groups

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Abstract

In the paper we propose a modification of the classical construction of the (Minkowskian) incidence structures based on permutation groups. Dropping out explicit assumptions concerning rigidity and transitivity (and assuming an arbitrary finite ”dimension”) we obtain a wider class of structures. Their geometrical properties are studied; in particular, we establish their automorphism groups and discuss some problems related to axiomatic characterization.

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Authors and Affiliations

  1. Division of Algebra and Geometry, University of Warmia and Mazury, ul. Żomierska 14 A, 10-561, Olsztyn, Poland

    Andrzej Matraś

  2. Institute of Mathematics, University of Bialystok, ul. Akademicka 2, 15-267, Bialystok, Poland

    Aneta Mierzejewska & Krzysztof Prazmowski

Authors
  1. Andrzej Matraś
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  2. Aneta Mierzejewska
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  3. Krzysztof Prazmowski
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Correspondence to Krzysztof Prazmowski.

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Matraś, A., Mierzejewska, A. & Prazmowski, K. Some chain geometries determined by transformation groups. Results. Math. 46, 251–270 (2004). https://doi.org/10.1007/BF03322886

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