Zur Archimedizität projektiver Ebenen über Cartesischen Gruppen
Consider an ordered projective plane \({\mathcal P}\). For any figure \({\mathfrak e}=(K,w,L,u)\) with \(u,w\neq K\cap L=v\in uw\neq K,L,\) the Archimedean property (of repeated left addition with respect to \({\mathfrak e})\) mean that the projectivity \(\pi_{{\mathfrak e}}=(K,w,L,u,K)\) has unbounded orbits on \(K\setminus v\). If \({\mathcal P}\) is \({\mathfrak e}\)-Archimedean for each figure \({\mathfrak e}\) containing a given line W, then \({\mathcal P}\) is already fully Archimedean. Weaker conditions suffice in planes of Lenz type \(\neq I\).
scientific article; zbMATH DE number 3951429