The structure of a collineation group preserving an oval in a projective plane of odd order

1995 ◽  
Vol 57 (1) ◽  
pp. 73-89 ◽  
Author(s):  
Mauro Biliotti ◽  
Gabor Korchmaros
Keyword(s):  
Projective Plane ◽  
Collineation Group ◽  
Odd Order

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 a conjecture of Hughes

1967 ◽  
Vol 63 (3) ◽  
pp. 647-652 ◽  
Author(s):  
Judita Cofman
Keyword(s):  
Projective Plane ◽  
Permutation Group ◽  
Translation Plane ◽  
Collineation Group ◽  
Affine Plane ◽  
Finite Projective Plane ◽  
Transitive Permutation Group ◽  
Condition C

D. R. Hughes stated the following conjecture: If π is a finite projective plane satisfying the condition: (C)π contains a collineation group δ inducing a doubly transitive permutation group δ* on the points of a line g, fixed under δ, then the corresponding affine plane πg is a translation plane.

Direct Product Decompositions of Elation Groups

1977 ◽  
Vol 20 (2) ◽  
pp. 173-182
Author(s):  
Julia M. Nowlin Brown
Keyword(s):  
Finite Field ◽  
Projective Plane ◽  
Direct Product ◽  
Collineation Group

Let G be a collineation group of a projective plane π. Let E be the subgroup generated by all elations in G. In the case that π is finite and G fixes no point or line, F. Piper [6; 7] has proved that if G contains certain combinations of perspectivities, then E is isomorphic to for some finite field g.

A Class of Non-Desarguesian Projective Planes

1957 ◽  
Vol 9 ◽  
pp. 378-388 ◽  
Author(s):  
D. R. Hughes
Keyword(s):  
Positive Integer ◽  
Projective Plane ◽  
Collineation Group ◽  
Difference Sets ◽  
Projective Planes ◽  
Desarguesian Projective Plane ◽  
Desarguesian Plane ◽  
Desarguesian Projective Planes

In (7), Veblen and Wedclerburn gave an example of a non-Desarguesian projective plane of order 9; we shall show that this plane is self-dual and can be characterized by a collineation group of order 78, somewhat like the planes associated with difference sets. Furthermore, the technique used in (7) will be generalized and we will construct a new non-Desarguesian plane of order p2n for every positive integer n and every odd prime p.

scholarly journals Generalization of Hall planes of odd order

1971 ◽  
Vol 4 (2) ◽  
pp. 205-209 ◽  
Author(s):  
P.B. Kirkpatrick
Keyword(s):  
Collineation Group ◽  
Projective Planes ◽  
Odd Order

Some properties of projective planes having a certain type of collineation group are proved, and a class of these planes which properly contains the class of all Hall planes of odd order is explicitly constructed.

On certain permutation representations of the Hall–Janko group

1988 ◽  
Vol 110 (3-4) ◽  
pp. 287-294 ◽  
Author(s):  
Alan R. Prince
Keyword(s):  
Projective Plane ◽  
Collineation Group ◽  
Finite Projective Plane ◽  
Janko Group

SynopsisCertain permutation representations of the Hall–Janko group J2 are studied. These representations are of interest in connection with the problem of whether J2 can act as astrongly irreducible collineation group of a finite projective plane.

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