Stabilizers of collineation groups of smooth stable planes
نویسندگان
چکیده
منابع مشابه
On collineation groups of finite planes
From the Introduction to P. Dembowski’s Finite Geometries, Springer, Berlin 1968: “ . . . An alternative approach to the study of projective planes began with a paper by BAER 1942 in which the close relationship between Desargues’ theorem and the existence of central collineations was pointed out. Baer’s notion of (p, L)–transitivity, corresponding to this relationship, proved to be extremely f...
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A subgroup of the linear translation complement of a translation plane is geometrically irreducible if it has no invariant lines or subplanes. A similar definition can be given for "geometrically primitive". If a group is geometrically primitive and solvable then it is fixed point free or metacyclic or has a normal subgroup 2a+b a of order w where w divides the dimension of the vector space. Si...
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An interesting problem in the foundations of geometry is the following question: What is the impact of the interplay of topological assumptions and homogeneity? One possibility to make this (rather philosophical) question treatable for a mathematician is the classiication project for stable planes. We shall brieey outline the necessary deenitions and basic (though occasionally deep) results. In...
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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...
متن کاملOn the Orbits of Collineation Groups
1. Introduction In this paper we consider some results on the orbits of groups of collineations, or, more generally, on the point and block classes of tactical decompositions, on symmetric balanced incomplete block designs (symmetric BIBD = (v, k, 2)-system=finite 2-plane), and we consider generalizations to (not necessarily symmetric) BIBD and other combinatorial designs. The results are about...
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ژورنال
عنوان ژورنال: Indagationes Mathematicae
سال: 1998
ISSN: 0019-3577
DOI: 10.1016/s0019-3577(98)80028-1