Spreads of orthogonal vector spaces are used to construct many translation planes of even order q, for odd m > 1, having a collineation with a (q − 1)-cycle on the line at infinity and on each of two affine lines.

Finite Universe Is our universe finite or infinite? As we travel further and further will our journey ever end or must we go on forever? The second possibility being frightening, it is convenient to assume the first. In other words, let us postulate that we live in the projective three-space. The quantum theorists have told us that matter, instead of being continuous, is discrete, so our univer...

Each generalized quadrangle (GQ) of order (q2, q) derived in the standard way from a conical flock via a q-clan with q = 2e has subquadrangles of order q associated with a family of q + 1 (not necessarily projectively equivalent) ovals in PG(2, q). A new family of these GQ is announced in [1] and named the Subiaco GQ. We begin a study of their collineation groups. When e is odd, e ≥ 5, the grou...

Kestenband proved in [12] that there are only seven pairwise non-isomorphic Hermitian intersections in the desarguesian projective plane PG…2; q† of square order q. His classi®cation is based on the study of the minimal polynomials of the matrices associated with the curves and leads to results of purely combinatorial nature: in fact, two Hermitian intersections from the same class might not be...

In this paper, we study projection systems with a single viewpoint, including combinations of mirrors and lenses (catadioptric) as well as just lenses with or without radial distortion (dioptric systems). Firstly, we extend a wellknown unifying model for catadioptric systems to incorporate a class of dioptric systems with radial distortion. Secondly, we provide a new representation for the imag...

A collineation group F of PG(d, q), d >= 3, which is transitive on lines is shown to be 2-transitive on points unless d = 4, q = 2 and ] F ] = 31'5. m m