Collineation Groups Which Are Primitive on an Oval of a Projective Plane of Odd Order
نویسندگان
چکیده
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.
منابع مشابه
Intransitive collineation groups of ovals fixing a triangle
We investigate collineation groups of a finite projective plane of odd order fixing an oval and having two orbits on it, one of which is assumed to be primitive. The situation in which there exists a fixed triangle off the oval is considered in detail. Our main result is the following. Theorem. Let p be a finite projective plane of odd order n containing an oval O: If a collineation group G of ...
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