A geometric characterization of elation Laguerre planes
An elation Laguerre plane is a Laguerre that admits a group of automorphisms in the kernel of the plane that acts regularly on the set of circles. The author shows that it suffices to require that for any two nonparallel points \(p\) and \(q\) the subgroup \(\Sigma_{[p,q]}\) in the kernel that fixes each point on the parallel classes of \(p\) and \(q\) acts regularly on the set of circles through \(p\) and \(q\), or equivalently, on each parallel class containing neither \(p\) nor \(q\). Generalising a result of \textit{A. E. Schroth} [Abh. Math. Semin. Univ. Hamb. 69, 211-227 (1999; Zbl 0953.51003)] the author further characterises elation Laguerre planes as the weakly Miquelian Laguerre planes, that is, those Laguerre planes in which a certain variation M2 of Miquel's configuration involving four pairs of parallel points is satisfied.
scientific article; zbMATH DE number 1742832