The elation group of a 4-dimensional Laguerre plane (Q1181783)

Let \({\mathcal L}=(P,{\mathcal K},\|)\) denote a 4-dimensional Laguerre plane and \(T\) denote the kernel of action of the automorphism group \(\Gamma\) of \(\mathcal L\) on the set of parallel classes \(\pi\). There are some characterizations of Laguerre planes with respect to the dimension of the kernel \(T\). The elation group \(\Delta\) is defined as \[ \Delta=\{\tau\in T\mid \tau \text{ fixes a parallel class pointwise}\}. \] In the main result of this paper the author describes the global structure of 4-dimensional Laguerre planes having a 6-dimensional elation group \(\Delta\).