On generalized André planes of dimension \(2(2n+1)\)
Let P be a proper generalized André plane (i.e. P is neither a Desarguesian plane nor a Hall plane). If P is finite, it is known that P has the following property: (*) there exist in P two special pencils of parallel lines fixed or exchanged by every collineation. It was an open question whether this property depends on the finite order or not. The author shows that P (not necessarily finite) has again the property (*) if P is of odd dimension and its homology groups fixing the above pencils have order \(\leq 2\). Yet the author shows in a more recent article (to appear in Geom. Dedicata) that this pattern cannot be expected to hold in the case of even dimension. In fact he gives an example of an (infinite) generalized André plane of dimension 4 which does not have the property (*).
scientific article; zbMATH DE number 3861912