Non-Existence of isomorphisms between certain unitals

We show that the Ree-Tits unitals are neither classical nor isomorphic to the polar unitals found in the Coulter-Matthews planes. To this end, we determine the full automorphism groups of the finite Ree-Tits unitals.     

On Restrictions of Automorphism Groups of Compact Projective Planes to Subplanes

It is shown that the restriction of automorphisms of a compact projective plane to a closed Baer subplane or to an open subgeometry, respectively, is a quotient mapping (in contrast to restrictions to arbitrary subgeometries). In the proof, we investigate lineations in towers of Baer subplanes.     

Polarities and planar collineations of Moufang planes

We show that conjugacy classes of Baer involutions and non-elliptic polarities, respectively, of proper (i.e., non-desarguesian) Moufang planes are interrelated. Restriction of the conjugating group to the stabilizer of a triangle or a quadrangle does not refine the classes. These results are applied to prove transitivity properties for the centralizers of these polarities. Along the way, a new proof is obtained for the fact that the automorphism group of a Moufang plane acts transitively on quadrangles.     

Linearly small elation quadrangles

We show that each elation generalized quadrangle with parameters (p, p), where p is a prime, is isomorphic to the symplectic quadrangle W(p) or its dual Q(4, p). Our results cover the more general case of linearly small elation generalized quadrangles. In particular, we obtain a characterization of the symplectic quadrangle over the field of complex numbers among compact connected quadrangles. We prove that every root elation quadrangle (Q, c, H _F ) is a skew translation quadrangle.     

Connected Orbits in Topological Generalized Quadrangles

We study generalized quadrangles. After an investigation of the subgeometries that are generated by arbitrary sets of vertices, we consider orbits of connected subgroups of the automorphism group of topological generalized quadrangles. We deal with the problem of how a set of vertices has to be chosen in order that the union of the orbits generates a subquadrangle, or even the whole quadrangle.