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Transitive affine planes admitting elations

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Abstract

Affine planes which admit a point transitive collineation group and at least one affine elation are considered. Such a plane is shown to be (A,ℓ∞)-transitive for some point A on ℓt8 and to be a translation plane if at least two distinct elation centers exist. If the plane has at least (order)1/2+1 distinct elation centers and the group generated by the elations is nonsolvable then the plane is either Desarguesian or Lüneburg-Tits.

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Authors and Affiliations

  1. Mathematics Dept., Kalamazoo College, Kalamazoo, Mich.

    J. B. Fink

  2. Mathematics Dept., University of Iowa, Iowa City, Ia.

    N. L. Johnson

  3. Mathematics Dept., University of Missouri, St. Louis, Mo.

    F. W. Wilke

Authors
  1. J. B. Fink
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  2. N. L. Johnson
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  3. F. W. Wilke
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Fink, J.B., Johnson, N.L. & Wilke, F.W. Transitive affine planes admitting elations. J Geom 21, 59–65 (1983). https://doi.org/10.1007/BF01918131

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  • DOI: https://doi.org/10.1007/BF01918131

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