On the Minkowski planes constructed by Artzy and Groh (Q998230)

A family of real Minkowski planes was constructed in [\textit{R. Artzy} and \textit{H. Groh}, J. Geom. 26, 1--20 (1986; Zbl 0598.51004)]. By construction, an Artzy Groh Minkowski plane contains a point \(w\) such that the affine derived plane at \(w\) is a translation plane such that every translation is the restriction of an automorphism of the original Minkowski plane. Furthermore, for a point \(p\) of the affine derived plane, the group of all automorphisms fixing each cycle through \(p\) and \(w\) decomposes each cycle through \(p\) and \(w\) (apart from \(\{p\}\) and \(\{w\}\)) in at most two orbits. In the paper the authors prove that these properties characterize the Artzy-Groh planes among the locally compact, connected and finite dimensional topological Minkowski planes. With exception of the Miquelian Minkowski planes over the reals, the automorphism group of the Artzy-Groh planes fixes the point \(w\). Finally, in [\textit{M. Klein}, J. Geom. 43, 116--128 (1992; Zbl 0746.51009)] the Minkowski planes were typified (19 different types) by determining the configurations of all \(2\)-sets of points \(\{p,q\}\) such that the Minkowski plane is \((p,q)-\)transitive. The types of the Artzy-Groh planes in the typification of Klein are determined in the paper.