A classification is given of all spreads in PG(3,#), q = 2, whose associated translation planes admit linear collineation groups of order q(q -hi) .

Let be a dense projective subplane of a topological projective plane. We show that a continuous homomorphism of is extendable to a continuous homomorphism of if and only if there is a line Z of such that the restriction of to the-points of Z is continuously extendable to some mapping deened on all-points of Z. In particular, each projective collineation of is extendable to a projective collinea...

If φ : L → L′ is a bijection from the set of lines of a linear space (P,L) onto the set of lines of a linear space (P ′,L′) (dim (P,L), dim (P ′,L′) ≥ 3), such that intersecting lines go over to intersecting lines in both directions, then φ is arising from a collineation of (P,L) onto (P ′,L′) or a collineation of (P,L) onto the dual linear space of (P ′,L′). However, the second possibility can...

In many applications, one is required to estimate the projective transformation between two sets of points, which is also known as collineation or homography. This report presents a number of techniques for this purpose.

An antiflag in a projective space is a non-incident point-hyperplane pair. A subgroup G of ΓL(n,q) is antiflag-transitive if it acts transitively on the set of antiflag of PG(n−1,q). In 1979, Cameron and Kantor [2] published a paper determining all antiflagtransitive subgroups of ΓL(n,q). A large part of the motivation was the fact that a group which acts 2-transitively on points is necessarily...

A classification is given of all spreads in PGð3; qÞ, q 1⁄4 2 , whose associated translation planes admit linear collineation groups of order qðqþ 1Þ.

It has been shown that relative projective shape, determined up to an unknown projective transformation, with respect to 5 reference points can be obtained from point-to-point correspondences of a pair of images; Affine shape up to an unknown affine transformation with respect to 4 points can be obtained from parallel projection. We show in this paper that afTine shape with respect to 4 referen...

We present a new framework for correcting multiperspective distortions using collineations. A collineation describes the transformation between the images of a camera due to changes in sampling and image plane selection. We show that image distortions in many previous models of cameras can be effectively reduced via proper collineations. To correct distortions in a specific multiperspective cam...

In [ 1 ] it was shown that there is no projective plane of order 12 which possesses a collineation group of order 12 consisting of elations with a fixed point as a center and a fixed line as its axis. We prove THEOREM A. There is no projective plane of order 12 which possesses a collineation group of order 4 consisting of elations with a fixed point as a center and a fixed line as its axis. Pro...

Let G be an abelian collineation group of order nðn 1Þ of a projective plane of order n. We show that n must be power of a prime p and that the p-part of G is elementary abelian.