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Transversal designs associated with frobenius groups

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Abstract

To any Frobenius group G (of degree s, with Frobenius complement of order k) we associate an (s,k) -transversal design Δ(G) which admits G as a point-regular collineation group. Δ(G) is in fact also a dual translation net and furthermore admits a flag-regular collineation group. Also, Δ(G) has two orthogonal resolutions. Conversely, we will characterize the Frobenius groups among the point-regular collineation groups of resolvable transversal designs. We also exhibit two further classes of flag-regular transversal designs. Finally, we completely determine the possible parameters of TD's constructed as above.

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Authors and Affiliations

  1. Mathematisches Institut, Justus-Liebig-Universität Gießen, Arndtstr. 2, D-6300, Gießen, F.R. Germany

    Dieter Jungnickel

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  1. Dieter Jungnickel
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Dedicated to Professor R. Artzy on the occasion of his 70th birthday

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Jungnickel, D. Transversal designs associated with frobenius groups. J Geom 17, 140–154 (1981). https://doi.org/10.1007/BF01951193

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  • DOI: https://doi.org/10.1007/BF01951193

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