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.

中文翻译：

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二维Laguerre平面的Kleinewillinghöfer类型的分类

Kleinewillinghöfer就中心自同构将Laguerre平面分类。Polster和Steinke研究了二维Laguerre平面及其所谓的Kleinewillinghöfer类型，即关于完全同构群的Kleinewillinghöfer类型。对于其中一种类型，存在问题仍然悬而未决。我们提供了此类IA2型平面的示例，这些示例是通过在IV.A.1型某些二维Laguerre平面之间交换一些圆而获得的。这样就完成了二维Laguerre平面Kleinewillinghöfer类型的分类。