Translation Plane

In mathematics, a translation plane is a particular kind of projective plane, as considered as a combinatorial object.

In a projective plane, represents a point, and represents a line. A central collineation with center and axis is a collineation fixing every point on and every line through . It is called an "elation" if is on, otherwise it is called a "homology". The central collineations with centre and axis form a group.

A projective plane is called a translation plane if there exists a line such that the group of elations with axis is transitive on the affine plane Πl (the affine derivative of Π).

Read more about Translation PlaneRelationship To Spreads

Other articles related to "translation plane, translation planes, planes":

Translation Plane - Relationship To Spreads
... Translation planes are related to spreads in finite projective spaces by the André/Bruck-Bose construction ... of, the André/Bruck-Bose construction1 produces a translation plane of order q2 as follows Embed as a hyperplane of ... "points," the points of not on and "lines" the planes of meeting in a line of ...

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