A new class of square order planes |
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Authors: | M.L Narayana Rao K Satyanarayana |
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Affiliation: | Department of Mathematics, Osmania University, Hyderabad 500 007, India |
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Abstract: | Only a few classes of square order planes are known. These are generalized André planes (including Hall planes), flag transitive planes, Hering's planes and Walker's planes. A new class of planes of order 52r, where r is an odd natural number, is constructed and the translation complements of the corresponding planes have been determined. The translation complements divide the sets of distinguished points into 4 orbits of lengths 1, 1, 5r ? 1, and 52r ? 5r and it is of order 5r(5r ? 1)2 if r ≠ 1. In the particular case of r = 1, the translation complement divides the set of distinguished points into two orbits of lengths 6 and 20 and it is of order 480. |
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