Irreducible collineation groups with two orbits forming an oval

Irreducible 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.

On 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...

Collineation 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.

On Finite Groups With Two Irreducible Character Degrees

Collineation Groups of the Intersection of Two Classical Unitals

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...