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Conics and Orthogonal Projectivities In a Finite Plane

Published online by Cambridge University Press:  20 November 2018

W. L. Edge
W. L. Edge*
Affiliation:
University of Edinburgh
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1. Introduction. The ternary orthogonal group of projectivities over a finite field leaves a non-singular conic ✗ invariant, but the geometry consequent thereupon does not appear to have been investigated. The group is isomorphic to a binary group of fractional substitutions over the same field and this fact may, since these binary groups and their subgroups are so well known, have inhibited projects to embark on a detailed description of the geometry of the ternary group.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 8 , 1956 , pp. 362 - 382
Copyright
Copyright © Canadian Mathematical Society 1956

References

1. Burnside, W., Theory of groups of finite order (Cambridge, 1911).Google Scholar
2. Clebsch, A., Über die Anwendung der quadratischen Substitution auf die Gleichung 5ten Grades und die geometrische Theorie des ebenen Fönfseits, Math. Ann., 4 (1871), 284–345.Google Scholar
3. Dickson, L. E., Linear groups, with an exposition of the Galois field theory (Leipzig, 1901).Google Scholar
4. Edge, W. L., Geometry in three dimensions over GF(3), Proc. Royal Soc. A222 (1953), 262–286.Google Scholar
5. Edge, W. L., 31-point geometry, Math. Gazette, 39 (1955), 113–121.Google Scholar
6. Galois, E., Lettre de Galois à M. Auguste Chevalier, J. de math, pures et appliquées, 11 (1846), 408–415.Google Scholar
7. Klein, F., Über die Transformation siebenter Ordnung der elliptischen Funktionen, Math Ann., 14 (1879), 428–471.Google Scholar
8. Klein, F., Vorlesungen öber des Ikosaëder (Leipzig, 1884).Google Scholar
9a, b. Klein, F. and Fricke, R., Vorlesungen öber die Theorie der elliptischen Modulfunktionen (Leipzig, 1890 and 1892).Google Scholar
10. Qvist, B., Some remarks concerning curves of the second degree in a finite plane. Annales Academiae Scientiarum Fennicae A., No. 134 (1952).Google Scholar
11. Serret, J. A., Cours d'algèbre supérieure (5th ed.), tome 2 (Paris, 1885).Google Scholar