Relationship To Spreads
Translation planes are related to spreads in finite projective spaces by the André/Bruck-Bose construction. A spread of is a set of q2 + 1 lines, with no two intersecting. Equivalently, it is a partition of the points of into lines.
Given a spread of, the André/Bruck-Bose construction1 produces a translation plane of order q2 as follows: Embed as a hyperplane of . Define an incidence structure with "points," the points of not on and "lines" the planes of meeting in a line of . Then is a translation affine plane of order q2. Let be the projective completion of .
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