In this article, the finite translation planes which are quadratic extensions of flag-transitive subplanes are classified as either Desarguesian or Hall.
โฆ LIBER โฆ
Flag-transitive Extensions of Dual Affine Planes
โ Scribed by Antonio Pasini
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 324 KB
- Volume
- 17
- Category
- Article
- ISSN
- 0195-6698
No coin nor oath required. For personal study only.
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For any odd prime power q, all (q 2 &q+1)th roots of unity clearly lie in the extension field F q 6 of the Galois field F q of q elements. It is easily shown that none of these roots of unity have trace &2, and the only such roots of trace &3 must be primitive cube roots of unity which do not belong
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The flag-transitive affine planes of order 125 are completely classified. There are five such planes.