On the finite projective planes of order up to q4, q odd, admitting PSL(3,q) as a collineation group
نویسندگان
چکیده
منابع مشابه
Projective Planes of Order 12 Do Not Have a Four Group as a Collineation Group
We have shown in [2] that the full collineation group of any projective plane of order 12 is a (2, 3) group. It is of interest to determine the structure of this (2,3} group. As a first step in that direction, we have shown in [3] that a non-Abelian group of order 6 cannot act as a collineation group on any projective plane of order 12. As a second step, we have shown in [4] that there is no pr...
متن کاملFinite Laguerre Near-planes of Odd Order Admitting Desarguesian Derivations
From this definition it readily follows that a Laguerre plane of order n has n + 1 generators, that every circle contains exactly n + 1 points and that there are n3 circles. All known models of finite Laguerre planes are of the following form. Let O be an oval in the Desarguesian projective plane P2 = PG(2, pm), p a prime. Embed P2 into threedimensional projective space P3 = PG(3, pm) and let v...
متن کاملOn projective planes of order 12 with a collineation group of order 9
In this paper, we prove that if π is a projective plane of order 12 admitting a collineation group G of order 9, then G is an elementary abelian group and is not planar.
متن کاملOn 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...
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.
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ژورنال
عنوان ژورنال: Innovations in Incidence Geometry: Algebraic, Topological and Combinatorial
سال: 2008
ISSN: 2640-7345,2640-7337
DOI: 10.2140/iig.2008.6.73