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Existence of parallelisms and projective extensions for strongly n-uniform near affine Hjelmslev planes

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Abstract

An affine Hjelmslev plane is a near affine Hjelmslev plane with a parallelism. It is proved that every strongly n-uniform near affine Hjelmslev plane possesses an even parallelism and, if n > 2, uneven parallelisms as well. Secondly, we prove that a strongly n-uniform affine Hjelmslev plane A has an extension to a strongly n-uniform projective Hjelmslev plane if and only if the parallelism of A is even. The above results are applied to yield the first known examples of affine Hjelmslev planes which possess no extensions to projective Hjelmslev planes.

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Authors and Affiliations

  1. Dept. of Mathematics, University of Florida, Gainesville, Fla., U.S.A.

    David A. Drake

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  1. David A. Drake
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This research was partially supported by National Science Foundation Research Grant GP-39059. matrix

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Drake, D.A. Existence of parallelisms and projective extensions for strongly n-uniform near affine Hjelmslev planes. Geom Dedicata 3, 191–214 (1974). https://doi.org/10.1007/BF00183210

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  • DOI: https://doi.org/10.1007/BF00183210

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