منابع مشابه
Point-primitive Inversive Planes of Odd Order
A famous but still unsolved problem in finite geometries is the question of whether a finite inversive plane J of odd order n is necessarily miquelian, that is, it arises from the plane sections of an elliptic quadric in PG(3,«). The question has been approached from different angles, and it has a positive answer if suitable conditions are added to J. The most classical result in this context i...
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 کاملOn the Order of Primitive Groups
At the end of a memoir on primitive groups in the first volume of the Bulletin of the Mathematical Society of France, f Jordan announced the following theorem : Let q be a poaitive integer leas than 6, p any prime number greater than q; the degree of a primitive group G that contains a subatitutitm of order p on q cyclea (without including the alternating group) cannot exceed pq + q + 1. The pr...
متن کاملMinimal Odd Order Automorphism Groups
We show that 3 is the smallest order of a non-trivial odd order group which occurs as the full automorphism group of a finite group.
متن کاملOn odd primitive graphs
In this paper, we prove that every odd primitive graph must contain two vertex disjoint odd cycles. We also characterize a family of odd primitive graphs whose exponent achieves the upper bound. We follow the notation and terminology of Bondy and Murty [1], unless otherwise stated. A digraph D is said to be primitive if there exists a positive integer k such that for each ordered pair of vertic...
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ژورنال
عنوان ژورنال: American Journal of Mathematics
سال: 1904
ISSN: 0002-9327
DOI: 10.2307/2369903