Classification of Minkowski planes by transitive groups of homotheties (Q1184579)

In 1989, the author with H.-J. Kroll published a classification of Minkowski planes based on the notions ``\(G\)-translations'' and ``\(q\)- translations''. In the present paper the author improves upon the classification by looking at transitive groups of homotheties. These results complete the classification by \textit{M. Meschiari} and \textit{P. Quattrocchi} for the finite planes [Atti Sem. Mat. Fis. Univ. Modena (1975), 123-141 (1976; Zbl 0328.50018)]. Finally, except two types, there are presented examples of groups of automorphisms of Minkowski planes for all classes of the classification.