A note on Minkowski planes admitting groups of automorphisms of some large types with respect to homotheties

Monica Klein classified Minkowski planes with respect to linearly transitive subgroups of Minkowski homotheties. She obtained 23 possible types. In this paper we investigate Minkowski planes with respect to groups of automorphism of certain Klein types 12 and higher. We show that types 12 and 14 can only occur in finite miquelian Minkowski planes of order 3 or 5, and we provide examples for such groups. Furthermore, we prove that types 13 and 18 in finite Minkowski planes can only occur in miquelian planes.