On 4-transitivity in the Moufang plane

Suleyman Ciftci; Rustem Kaya; Joseph C. Ferrar

doi:10.1007/bf01222385

On 4-transitivity in the Moufang plane

Journal of Geometry ◽

10.1007/bf01222385 ◽

1988 ◽

Vol 31 (1-2) ◽

pp. 65-68 ◽

Cited By ~ 1

Author(s):

Suleyman Ciftci ◽

Rustem Kaya ◽

Joseph C. Ferrar

Keyword(s):

Moufang Plane

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Products of Reflections in an Affine Moufang Plane

Canadian Journal of Mathematics ◽

10.4153/cjm-1970-073-6 ◽

1970 ◽

Vol 22 (3) ◽

pp. 666-673 ◽

Cited By ~ 4

Author(s):

K. Martin Götzky

Keyword(s):

Moufang Plane

Let be a Moufang plane. By specializing one line ω, the line at infinity, weobtain an affine Moufang plane . The group generated by the shears of is called the equiaffine group. Veblen [9, § 52] asked whether every equiaffinity is a product of two affine reflections. He gave a proof which will work in an affine Pappian plane, using the following two properties.Property 1. If an equiaffinity fixes two distinct proper points of , it fixes every point collinear with them.Property 2. Let e be an equiaffinity and P a point such that ppe2pe3 is a triangle. Then the lines PePe2 and PPe3 are parallel.Without using these properties, it will be proved that the answer to Veblen's question is “yes“ if and only if the Moufang plane is Pappian.

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

Canadian Journal of Mathematics ◽

10.4153/cjm-1987-045-4 ◽

1987 ◽

Vol 39 (4) ◽

pp. 908-919 ◽

Cited By ~ 6

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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