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A note on the Kleinewillinghöfer types of 4-dimensional Laguerre planes

  • Günter F. Steinke
Published/Copyright: October 19, 2022
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Abstract

Kleinewillinghöfer classified in 1979 automorphism groups of Laguerre planes with respect to linearly transitive subgroups of central automorphisms and obtained a multitude of types. All feasible Kleinewillinghöfer types of 2-dimensional Laguerre planes were completely determined in 2021. In this paper we investigate the Kleinewillinghöfer types of 4-dimensional Laguerre planes with respect to the automorphism groups of these planes and show that of the 49 types Kleinewillinghöfer described, only twelve are feasible in 4-dimensional Laguerre planes. Examples of four of these type are provided.

MSC 2010: 51H15; 51B15
  1. Communicated by: R. Löwen

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Received: 2022-06-16
Published Online: 2022-10-19
Published in Print: 2022-10-26

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