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Affine Subplanes of Finite Projective Planes

Published online by Cambridge University Press:  20 November 2018

J. F. Rigby
J. F. Rigby*
Affiliation:
University of Toronto
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Let π be a finite projective plane of order n containing a finite projective subplane π* of order u < n. Bruck has shown (1, p. 398) that if π contains a point that does not lie on any line of π*, then n ≥ u2 + u, while if every point of π lies on a line of π* then n = u2.

Let π be a finite projective plane of order n containing a finite affine subplane π0 of order m < n.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 17 , 1965 , pp. 977 - 1009
Copyright
Copyright © Canadian Mathematical Society 1965

References

1. Hall, Marshall Jr., The theory of groups (New York, 1959).Google Scholar
2. Hall, Marshall Jr., Uniqueness of the projective plane with 57 points, Proc. Amer. Math. Soc, 4 (1953), 912–916.Google Scholar
3. Hall, Marshall Jr., Correction to u Uniqueness of the projective plane with 67 points,” Proc. Amer. Math Soc, 5 (1954), 994–997.Google Scholar
4. Hall, M., Swift, J. D., and Walker, R., Uniqueness of the projective plane of order eight, Math. Tables Aids Comput, 10 (1956), 186–194.Google Scholar
5. Ostrom, T. G. and Sherk, F. A., Finite projective planes with affine subplanes, Can. Math. Bull., 7 (1964), 549–560.Google Scholar