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The classification of Kleinewillinghöfer types of 2-dimensional Laguerre planes

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Abstract

Kleinewillinghöfer classified Laguerre planes with respect to central automorphisms. Polster and Steinke investigated 2-dimensional Laguerre planes and their so-called Kleinewillinghöfer types, that is, the Kleinewillinghöfer types with respect to the full automorphism group. For one of these types the existence question remained open. We provide examples of such planes of type I.A.2, which are obtained by interchanging some circles between certain 2-dimensional Laguerre planes of type IV.A.1. This completes the classification of Kleinewillinghöfer types of 2-dimensional Laguerre planes.

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  1. School of Mathematics and Statistics, University of Canterbury, Private Bag 4800, Christchurch, 8140, New Zealand

    Günter F. Steinke

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  1. Günter F. Steinke
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Correspondence to Günter F. Steinke.

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Steinke, G.F. The classification of Kleinewillinghöfer types of 2-dimensional Laguerre planes. Aequat. Math. 95, 967–983 (2021). https://doi.org/10.1007/s00010-021-00780-3

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