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Open Access
Semiaffine stable planes
(2023) Löwen, Rainer; Stroppel, Markus J.
A locally compact stable plane of positive topological dimension will be called semiaffine if for every line L and every point p not in L there is at most one line passing through p and disjoint from L . We show that then the plane is either an affine or projective plane or a punctured projective plane (i.e., a projective plane with one point deleted). We also compare this with the situation in general linear spaces (without topology), where P. Dembowski showed that the analogue of our main result is true for finite spaces but fails in general.
Open Access
Unitals with many involutory translations
(2023) Grundhöfer, Theo; Stroppel, Markus J.; Maldeghem, Hendrik van
If every point of a unital is fixed by a non-trivial translation and at least one translation has order two then the unital is classical (i.e., hermitian).
Open Access
Finite subunitals of the hermitian unitals
(2022) Grundhöfer, Theo; Stroppel, Markus J.; Maldeghem, Hendrik van
Every finite subunital of any generalized hermitian unital is itself a hermitian unital; the embedding is given by an embedding of quadratic field extensions. In particular, a generalized hermitian unital with a finite subunital is a hermitian one (i.e., it originates from a separable field extension).