On the Klein–Kroll types of flat Minkowski planes

Abstract

Klein and Kroll classified Minkowski planes with respect to subgroups of central automorphisms and obtained a multitude of types. Some of these types are known to exist only in finite Minkowski planes or as the type of a proper subgroup in the automorphism group. In this paper we investigate the Klein–Kroll types of flat Minkowski planes with respect to the full automorphism groups of these planes and completely determine all possible types of flat Minkowski planes. For each of these 14 types except type II.A.15 examples are given.