A note on Laguerre translations

Abstract

Using the correspondence between $2n$-dimensional Laguerre planes and compact antiregular generalized quadrangles with parameter $n=1,2$ we show that almost each automorphism of such a Laguerre plane that induces a translation in the derived affine plane at a point $p$ is a Laguerre translation, that is, fixes all points on the parallel class of $p$. The same is true for ovoidal Laguerre planes over ovals that also are dual ovals.