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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
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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
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5. Ostrom, T. G. and Sherk, F. A., Finite projective planes with affine subplanes, Can. Math. Bull., 7 (1964), 549–560.Google Scholar