scholarly journals The general structure of the projective planes admitting PSL(2,q) as a collineation group

2007 ◽  
Vol 5 (1) ◽  
pp. 35-116 ◽  
Author(s):  
Alessandro Montinaro
Keyword(s):  
Collineation Group ◽  
General Structure ◽  
Projective Planes

A New Kind of Free Extension for Projective Planes

1962 ◽  
Vol 5 (2) ◽  
pp. 167-170 ◽  
Author(s):  
Seymour Ditor
Keyword(s):  
General Structure ◽  
Projective Planes ◽  
Line Incident ◽  
Free Extension ◽  
Extensive Class ◽  
Partial Plane ◽  
Set Of Points

Marshall Hall [l] shows how projective planes of very general structure may be constructed and at the same time exhibits an extensive class which are non-Desarguesian. Here we shall indicate how his method of free extension can be generalized to yield a class of planes which seem to be distinct from those which he obtains.A partial plane is a system consisting of two distinct sets of elements, a set of "points" P, Q,… and a set of "lines" l, m,…, and a relation between these two sets, called "incidence", such that for any two distinct points, there is at most one line incident with both (or, equivalently, for any two distinct lines, there is at most one point incident with both). A partial plane is complete if every two distinct points are joined by a line and every two distinct lines intersect in a point.

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.

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