Linear collineation groups preserving an arc in a Möbius plane
نویسندگان
چکیده
منابع مشابه
Collineation Groups Preserving a Unital in a Projective Plane of Order
A unital embedded in a finite projective plane Π of order m# is a substructure of Π which forms a 2®(m$1,m1, 1) design. Several authors devoted their attention to the embedded unitals. The main aim is either to construct and investigate new classes of unitals, or to characterize some classes using group-theoretical or graphical properties [3, 6, 9, 18, 25]. In [3] we give some general results...
متن کاملCollineation Groups Which Are Primitive on an Oval of a Projective Plane of Odd Order
It is shown that a projective plane of odd order, with a collineation group acting primitively on the points of an invariant oval, must be desarguesian. Moreover, the group is actually doubly transitive, with only one exception. The main tool in the proof is that a collineation group leaving invariant an oval in a projective plane of odd order has 2-rank at most three.
متن کاملAntiflag-transitive collineation groups revisited
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 کاملIrreducible collineation groups with two orbits forming an oval
Let G be a collineation group of a finite projective plane π of odd order fixing an oval Ω . We investigate the case in which G has even order, has two orbits Ω0 and Ω1 on Ω , and the action of G on Ω0 is primitive. We show that if G is irreducible, then π has a G-invariant desarguesian subplane π0 and Ω0 is a conic of π0. © 2007 Elsevier Inc. All rights reserved.
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: Discrete Mathematics
سال: 1999
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(99)90141-3