Points will always be denoted by small latin letters, lines by capitals (unlike Bonisoli’s notations). By (a, b), with a, b ∈ N, we denote the greatest common divisor of a and b. Suppose π is a projective plane of order n, and suppose (p, L) is a point-line pair. Then a collineation θ of π is a (p, L)-collineation if θ fixes any point on L and every line through p. If (p, L) is a flag, then θ i...

We establish the connections between finite projective planes admitting a collineation group of Lenz-Barlotti type 1.3 or 1.4, partially transitive planes of type (3) in the sense of Hughes, and planes admitting a quasiregular collineation group of type (g) in the DembowskiPiper classification; our main tool is an equivalent description by a certain type of difference set relative to disjoint s...

In this note, we outline a method which reduces the determination of the collineation group of a division ring plane to the solution of certain algebraic problems—in particular, to the question of when two rings of a certain type are isomorphic. This method is then applied to planes coordinatized by finite dimensional Jordan algebras of characteristic 5^2, 3, and their collineation groups are d...

Let ∆ be a thick building of type Xn = Cn,Dn. Let also Gk be the Grassmannian of k-dimensional singular subspaces of the associated polar space Π (of rank n). We write Gk for the corresponding shadow space of type Xn,k. Every bijective transformation of Gk preserving the class of base subsets (the shadows of apartments) is a collineation of Gk, and it is induced by a collineation of Π if n 6= 4...

A Subiaco hyperoval in PG(2, 2h), h ≥ 4, is known to be stabilised by a group of collineations induced by a subgroup of the automorphism group of the associated Subiaco generalised quadrangle. In this paper, we show that this induced group is the full collineation stabiliser in the case h 6≡ 2 (mod 4); a result that is already known for h ≡ 2 (mod 4). In addition, we consider a set of 2h + 2 po...

Let Π be a finite projective plane admitting a large abelian collineation group. It is well known that this situation may be studied by algebraic means (via a representation by suitable types of difference sets), namely using group rings and algebraic number theory and leading to rather strong nonexistence results. What is less well-known is the fact that the abelian group (and sometimes its gr...

In this paper we describe a method for estimating the internal parameters of the left and right cameras associated with a stereo image pair. The stereo pair has known epipolar geometry and therefore 3-D projective reconstruction of pairs of matched image points is available. The stereo pair is allowed to move and hence there is a collineation relating the two projective reconstructions computed...

Apart from hyperovals and their duals there are only three classes of maximal arcs known in Desarguesian projective planes. Two classes are due to J. A. Thas and one to R. H. F. Denniston. In this paper collineation stabiliser and isomorphism problems for those maximal arcs in Desarguesian projective planes are examined. The full collineation stabilisers of the known maximal arcs are calculated...