The full collineation group of any projective plane of order 12 is a {2, 3}-group

1982 ◽  
Vol 12 (1) ◽  
pp. 101-110 ◽  
Author(s):  
Zvonimir Janko ◽  
Tran Van Trung
Keyword(s):  
Projective Plane ◽  
Collineation Group ◽  
Full Collineation Group

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.

Every group is the collineation group of some projective plane

1976 ◽  
pp. 175-182 ◽  
Author(s):  
E. Mendelsohn
Keyword(s):  
Projective Plane ◽  
Collineation Group

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.

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

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 A translation plane of order 25 and its full collineation group

1978 ◽  
Vol 19 (3) ◽  
pp. 351-362 ◽  
Author(s):  
M.L. Narayana Rao ◽  
K. Kuppuswamy Rao
Keyword(s):  
Translation Plane ◽  
Collineation Group ◽  
Translation Planes ◽  
Single Orbit ◽  
Full Collineation Group ◽  
Ideal Points ◽  
The Ideal

Ostrom proposed classifications of translation planes on the basis of the action of the collineation group of the plane on the ideal points. There are examples of translation planes in which ideal points form a single orbit (flag transitive planes) and also several orbits (Hall, André, Foulser, and so forth, planes). In this paper the authors have constructed a translation plane in which the ideal points are divided into two orbits of lengths 18 and 8 respectively. A few collineatlons are computed together with their actions. The group of collineations G1 which is transitive on the two sets of 18 and 8 lines separately is calculated. All the collineations that fix L0 are also calculated and they form a group of. If G2 is the group of translations then the full collineation group is shown to be 〈G1, G2, G3〉.

THE HALL-JANKO GROUP AS A COLLINEATION GROUP OF AN INFINITE PROJECTIVE PLANE

1989 ◽  
Vol 40 (1) ◽  
pp. 93-100 ◽  
Author(s):  
ALAN R. PRINCE
Keyword(s):  
Projective Plane ◽  
Collineation Group ◽  
Janko Group

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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