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Ovals In a Finite Projective Plane

Published online by Cambridge University Press:  20 November 2018

Beniamino Segre*
Affiliation:
University of Rome
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1. Let be a finite projective plane (8, §17), i.e. a projective space of dimension 2 over a Galois field γ. We suppose that γ has characteristic p ≠ 2, hence order q = pn , where p is an odd prime and h is a positive integer. It is well known that every straight line and every non-singular conic of then contains q + 1 points exactly.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1955

References

1. Järnefelt, G., A plane geometry with a finite number of elements, Verröf. Finnischen Geodatischen Inst., 36 (1949), 7180.Google Scholar
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3. Järnefelt, G. and Kustaanheimo, P., An observation on finite geometries, Den l1te Skandinaviske Matematikerkongress, Trondheim (1949), 166182.Google Scholar
4. Kustaanheimo, P., A note on a finite approximation of the Euclidean plane geometry, Soc. Sci. Fenn. Comm. Phys. Math., 15, n. 19 (1950), 11 pp.Google Scholar
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6. Kustaanheimo, P. and Qvist, B., On differentiation in Galois fields, Ann. Acad. Sci. Fennicae (A, I), 137 (1952), 12 pp.Google Scholar
7. Qvist, B., Some remarks concerning curves of the second degree in a finite plane, Ann. Acad. Sci. Fennicae (A, I), 134 (1952), 27 pp.Google Scholar
8. Segre, B., Lezioni di geometria moderna, vol. 1 (Bologna, 1948).Google Scholar
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