Generalized polygons with highly transitive collineation groups (Q1900112)

The paper investigates compact connected topological generalized \(n\)-gons where the full collineation group acts transitively on the set of ordered \((n + 1)\)-gons. The main result states that only the classical polygons arise. Only generalized quadrangles have to be considered in more detail, since for the other possibilities, namely compact connected topological generalized triangles and hexagons, one knows all such polygons where the collineation group acts flag transitively. For generalized quadrangles all Moufang quadrangles are studied. It is shown that only the classical ones allow a group acting transitively on the set of ordered pentagons. The text is well structured and the material is presented in a very nice fashion.