Topological affine planes composed of two desarguesian halfplanes and projective planes with trivial collineation group

1985 ◽  
Vol 44 (5) ◽  
pp. 472-480 ◽  
Author(s):  
G�nter F. Steinke
Keyword(s):  
Collineation Group ◽  
Projective Planes ◽  
Affine Planes ◽  
Topological Affine

Finite Affine Planes and Projective Planes

2020 ◽  
pp. 11-16
Author(s):  
Michael A. Henning ◽  
Anders Yeo
Keyword(s):  
Projective Planes ◽  
Affine Planes ◽  
Finite Affine

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.

Four-Dimensional Compact Projective Planes with Collineation Group N6,28

1995 ◽  
Vol 28 (1-2) ◽  
pp. 100-116
Author(s):  
Hauke Klein
Keyword(s):  
Collineation Group ◽  
Projective Planes ◽  
Compact Projective Planes

scholarly journals The nonexistence of projective planes of order 12 with a collineation group of order 16

2004 ◽  
Vol 107 (1) ◽  
pp. 21-48 ◽  
Author(s):  
Chihiro Suetake
Keyword(s):  
Collineation Group ◽  
Projective Planes

scholarly journals Convexity in Topological Affine Planes

2007 ◽  
Vol 38 (2) ◽  
pp. 243-257 ◽  
Author(s):  
Raghavan Dhandapani ◽  
Jacob E. Goodman ◽  
Andreas Holmsen ◽  
Richard Pollack ◽  
Shakhar Smorodinsky
Keyword(s):  
Affine Planes ◽  
Topological Affine

The nonexistence of projective planes of order 12 with a collineation group of order 8

2008 ◽  
Vol 16 (5) ◽  
pp. 411-430 ◽  
Author(s):  
Kenzi Akiyama ◽  
Chihiro Suetake
Keyword(s):  
Collineation Group ◽  
Projective Planes

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.

Compactness in Topological Hjelmslev Planes

1984 ◽  
Vol 27 (4) ◽  
pp. 423-429 ◽  
Author(s):  
J. W. Lorimer
Keyword(s):  
Projective Plane ◽  
Affine Plane ◽  
Projective Planes ◽  
Coordinate Ring ◽  
Locally Compact ◽  
Compact Projective Plane ◽  
Negative Results ◽  
Connected Projective Plane ◽  
Topological Affine

AbstractIn the theory of ordinary topological affine and projective planes it is known that (1) An affine plane is never compact (2) a locally compact ordered projective plane is compact and archimedean (3) a locally compact connected projective plane is compact and (4) a locally compact projective plane over a coordinate ring with bi-associative multiplication is compact. In this paper we re-examine these results within the theory of topological Hjelmslev Planes and observe that while (1) remains valid (2), (3) and (4) are false. At first glance these negative results seem to suggest we are working in too general a setting. However a closer examination reveals that the absence of compactness in our setting is a natural and expected feature which in no way precludes the possibility of obtaining significant results.

Flat projective planes with 2-dimensional collineation group fixing at least two lines and more than two points

1990 ◽  
Vol 38 (1-2) ◽  
pp. 107-157 ◽  
Author(s):  
Hans-Joachim Pohl
Keyword(s):  
Collineation Group ◽  
Projective Planes
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