Abstract
We characterize the non-classical 4-dimensional elation Laguerre planes as precisely those 4-dimensional Laguerre planes of Kleinewillinghofer type I.D.1. Furthermore, in the class of 2- or 4-dimensional Laguerre planes or finite Laguerre planes of odd order, the non-miquelian elation Laguerre planes are precisely the Laguerre planes of Kleinewillinghofer type D.
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