4-dimensional compact projective planes with a 7-dimensional collineation group

1990 ◽  
Vol 36 (2-3) ◽  
Author(s):  
Dieter Betten
Keyword(s):  
Collineation Group ◽  
Projective Planes ◽  
Compact Projective Planes

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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