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Über ebene affine Inzidenzgruppen

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Abstract

For a translation plane P with respect to f we consider the group of collineations Σ generated by all elations fixing f and a point F of f. All subgroups Γ or Σ are determined which operate regularly on the points of the affine plane P. Group-theoretic and operating properties of the groups Γ are stated especially for the finite and the Desarguesian cases. In the latter case the companion NL-near modules are constructed. Finally we characterize the groups Γ within PGL(3, K) with commutative field K of finite characteristic.

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Authors and Affiliations

  1. Fachbereich 6 Mathematik, Universität Oldenburg, D-2900, Oldenburg, Deutschland

    Irene Pieper-seier

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  1. Irene Pieper-seier
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Pieper-seier, I. Über ebene affine Inzidenzgruppen. Geom Dedicata 22, 1–20 (1987). https://doi.org/10.1007/BF00183050

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  • DOI: https://doi.org/10.1007/BF00183050

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