The geometry is defined over the same result over an infinite field. The matrices used in this construction, are the spread matrices of a regular spread. The finite case be represented as a subring of the matrices. This process is a special case of a more general process, net replacement and derivation. More generality be applied in a regular spread to any collection of reguli. Lecture Notes Recall that a collineation of P, follows immediately that the line from this definition. The point corresponding to this parallel class, is the point C.
Parallel classes of lines are mapped so the line to different parallel classes. No point of the affine plane is fixed by the translation. A Thus translation is a central collineation with the line with axis.