Compact 16-dimensional projective planes with large collineation groups

1982 ◽  
Vol 261 (4) ◽  
pp. 447-454 ◽  
Author(s):  
H. Salzmann
Keyword(s):  
Projective Planes ◽  
Collineation Groups

scholarly journals Homomorphisms of sharply transitive projective planes

1971 ◽  
Vol 4 (3) ◽  
pp. 361-366 ◽  
Author(s):  
Don Row
Keyword(s):  
Projective Planes ◽  
Collineation Groups ◽  
Sharply Transitive

We construct projective planes having non-degenerate homomorphic images, the homomorphisms preserving certain sharply transitive collineation groups.

On collineation groups of projective planes of order n = −l (Mod 6)

1985 ◽  
Vol 13 (7) ◽  
pp. 1509-1534 ◽  
Author(s):  
Adilson Gonçalves ◽  
Danilo F. Barboza
Keyword(s):  
Projective Planes ◽  
Collineation Groups

Compact 16-Dimensional Projective Planes with Large Collineation Groups. IV

1987 ◽  
Vol 39 (4) ◽  
pp. 908-919 ◽  
Author(s):  
Helmut Salzmann
Keyword(s):  
Transformation Group ◽  
Projective Planes ◽  
Finite Covering ◽  
Covering Dimension ◽  
Topological Projective Plane ◽  
Collineation Groups ◽  
Compact Transformation Group ◽  
Point Set ◽  
Type V ◽  
Moufang Plane

Let be a topological projective plane with compact point set P of finite (covering) dimension. In the compact-open topology (of uniform convergence), the group Σ of continuous collineations of is a locally compact transformation group of P.THEOREM. If dim Σ > 40, thenis isomorphic to the Moufang plane 6 over the real octonions (and dim Σ = 78).By [3] the translation planes with dim Σ = 40 form a one-parameter family and have Lenz type V. Presumably, there are no other planes with dim Σ = 40, cp. [17].

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