Search results for "Collineation"

Multiplicative loops of 2-dimensional topological quasifields

2015

We determine the algebraic structure of the multiplicative loops for locally compact $2$-dimensional topological connected quasifields. In particular, our attention turns to multiplicative loops which have either a normal subloop of positive dimension or which contain a $1$-dimensional compact subgroup. In the last section we determine explicitly the quasifields which coordinatize locally compact translation planes of dimension $4$ admitting an at least $7$-dimensional Lie group as collineation group.

Correction to ?partial spreads in finite projective spaces and partial designs?

1976

On Baer subspaces of finite projective spaces

1983

Zur Hyperebenenalgebraisierung in desargues-Schen projektiven Verbandsgeometrien

1991

As a completion and extension of a result of A. Day and D. Pickering [5] we obtain the following structure theorem in the conceptual frame of projective lattice geometries: In a Desarguesian projective geometry the subgeometry of every at least one-dimensional hyperplane is module induced.

Partial spreads in finite projective spaces and partial designs

1975

A partial t-spread of a projective space P is a collection 5 p of t-dimensional subspaces of P of the same order with the property that any point of P is contained in at most one element of 50. A partial t-spread 5 p of P is said to be a t-spread if each point of P is contained in an element of 5P; a partial t-spread which is not a spread will be called strictly partial. Partial t-spreads are frequently used for constructions of affine planes, nets, and Sperner spaces (see for instance Bruck and Bose [5], Barlotti and Cofman [2]). The extension of nets to affine planes is related to the following problem: When can a partial t-spread 5 ~ of a projective space P be embedded into a larger part…

On t-covers in finite projective spaces

1979

A t-cover of the finite projective space PG(d,q) is a setS of t-dimensional subspaces such that any point of PG(d,q) is contained in at least one element ofS. In Theorem 1 a lower bound for the cardinality of a t-coverS in PG(d,q) is obtained and in Theorem 2 it is shown that this bound is best possible for all positive integers t,d and for any prime-power q.

Projective spaces on partially ordered sets and Desargues' postulate

1991

We introduce a generalized concept of projective and Desarguean space where points (and lines) may be of different size. Every unitary module yields an example when we take the 1-and 2-generated submodules as points and lines. In this paper we develop a method of constructing a wide range of projective and Desarguean spaces by means of lattices.

A class of unitals of order q which can be embedded in two different planes of order q2

1987

By deriving the desarguesian plane of order q2 for every prime power q a unital of order q is constructed which can be embedded in both the Hall plane and the dual of the Hall plane of order q2 which are non-isomorphic projective planes. The representation of translation planes in the fourdimensional projective space of J. Andre and F. Buekenhouts construction of unitals in these planes are used. It is shown that the full automorphism groups of these unitals are just the collineation groups inherited from the classical unitals.

Kollineationen und Schliessungssätze für Ebene Faserungen

1979

Every affine central collineation of a translation plane π induces a special collineation of the projective space π spanned by the spreadF belonging to π. Here the relations between these special collineations of π and certain incidence propositions inF are investigated; so new proofs are given for some characterisations of (A,B)-regular spreads included in [7].

On some Translation Planes Admitting a Frobenius Group of Collineations

1983

Publisher Summary This chapter presents some results concerning translation planes of dimension 2 over GF(q), where q = p r . π denotes such a plane. It is assumed that π has a collineation group F of order q 2 (q-1) satisfying the condition: there exists a point V e l ∞ such that F fixes V and acts (faithfully) as a Frobenius group on l ∞ – {V}.