On collineation groups of a projective plane of prime order

1986 ◽  
Vol 20 (3) ◽  
Author(s):  
ChatYin Ho ◽  
Adilson Goncalves
Keyword(s):  
Projective Plane ◽  
Prime Order ◽  
Collineation Groups

scholarly journals Collineation groups preserving an oval in a projective place of odd order

1990 ◽  
Vol 48 (1) ◽  
pp. 156-170 ◽  
Author(s):  
Mauro Biliotti ◽  
Gabor Korchmaros
Keyword(s):  
Projective Plane ◽  
Collineation Group ◽  
Finite Projective Plane ◽  
Odd Order ◽  
Collineation Groups

AbstractIn this paper we investigate the structure of a collineation group G of a finite projective plane Π of odd order, assuming that G leaves invariant an oval Ω of Π. We show that if G is nonabelian simple, then G ≅ PSL(2, q) for q odd. Several results about the structre and the action of G are also obtained under the assumptions that n ≡ 1 (4) and G is transitive on the points of Ω.

On Baer Involutions of Finite Projective Planes

1970 ◽  
Vol 22 (4) ◽  
pp. 878-880 ◽  
Author(s):  
Judita Cofman
Keyword(s):  
Projective Plane ◽  
Finite Projective Plane ◽  
Projective Planes ◽  
Desarguesian Projective Plane ◽  
Finite Projective Planes ◽  
Special Cases ◽  
Collineation Groups ◽  
Baer Involution ◽  
Finite Desarguesian Projective Plane

1. An involution of a projective plane π is a collineation X of π such that λ2 = 1. Involutions play an important röle in the theory of finite projective planes. According to Baer [2], an involution λ of a finite projective plane of order n is either a perspectivity, or it fixes a subplane of π of order in the last case, λ is called a Baer involution.While there are many facts known about collineation groups of finite projective planes containing perspectivities (see for instance [4; 5]), the investigation of Baer involutions seems rather difficult. The few results obtained about planes admitting Baer involutions are restricted only to special cases. Our aim in the present paper is to investigate finite projective planes admitting a large number of Baer involutions. It is known (see for instance [3, p. 401]) that in a finite Desarguesian projective plane of square order, the vertices of every quadrangle are fixed by exactly one Baer involution.

Collineation Groups Containing Perspectivities

1967 ◽  
Vol 19 ◽  
pp. 924-937 ◽  
Author(s):  
Peter Dembowski
Keyword(s):  
Projective Plane ◽  
Finite Order ◽  
Translation Plane ◽  
Collineation Groups

Let P be a projective plane of finite order n and Γ a group of collineations of P. Gleason (6) and Wagner (10) have shown that if every point of P is the centre, and every line the axis, of a non-trivial perspectivity in Γ, then Γ contains a subgroup of order n2 which consists entirely of elations. It then follows that either P or its dual is a translation plane with respect to at least one line; in fact if Γ has no fixed elements, then P is desarguesian and Γ contains all elations of P. It was shown by Piper (7) and Cofman (4) that the hypotheses of Gleason and Wagner can be relaxed in certain cases, while the same conclusions hold.

scholarly journals Collineation groups preserving a unital of a projective plane of odd order

1989 ◽  
Vol 122 (1) ◽  
pp. 130-149 ◽  
Author(s):  
Mauro Biliotti ◽  
Gabor Korchmaros
Keyword(s):  
Projective Plane ◽  
Odd Order ◽  
Collineation Groups
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