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On The Projective Plane Pg (2, 3) | ||
| Tikrit Journal of Pure Science | ||
| Article 1, Volume 13, Issue 3, 2008, Pages 59-61 | ||
| Author | ||
| Esam R. Kakayee | ||
| Abstract | ||
| In this work it is shown that the Steiner system S (2, 4, 13) (the projective plane of order three) can be constructed from the Steiner system S (5, 6, 12), by adding a new point to its twelve points.The third contraction of S (5, 6, 12) with respect to the same triads defined in (Kakayee, 1990) respectively yields four Steiner systems S (2, 3, 9) (the affine plane of order three), denoted by . In order to construct the same projective plane (without any isomorphic forms in case of using Singers theorem) considered in (Kakayee, 1990), the following procedure was used:- i- (9) Blocks formed from the union of all blocks of that intersect in two points, ii- (4) blocks formed from the union of all blocks of that intersect in three points each with a new point. | ||
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