Minkowski semi-planes (Q1823467)

The paper is concerned with finite Minkowski semi-planes \({\mathfrak M}\) which are defined by axioms that are a little more general than those of finite Minkowski planes and finite Minkowski-near planes: Generators are allowed to have either n or \(n+1\) points, where n denotes the order of the plane, and two different generators or a block and a generator may have at most one common point. If any two generators of different classes intersect, then \({\mathfrak M}\) is shown to be a Minkowski near-plane of order \(n+1\), or a Minkowski plane of order n with one generator deleted, or a Minkowski plane of order n-1. If \({\mathfrak M}\) has non-intersecting generators of different classes, then \({\mathfrak M}\) is either (n\(\geq 4)\) a Minkowski-plane of order n with one point deleted or \((n=2,3)\) one of the structures given explicitely in the paper.