Finite Projective Planes with Affine Subplanes
1964 ◽
Vol 7
(4)
◽
pp. 549-559
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Keyword(s):
A well-known theorem, due to R. H. Bruck ([4], p. 398), is the following:If a finite projective plane of order n has a projective subplane of order m < n, then either n = m2 or n > m 2+ m.In this paper we prove an analagous theorem concerning affine subplanes of finite projective planes (Theorem 1). We then construct a number of examples; in particular we find all the finite Desarguesian projective planes containing affine subplanes of order 3 (Theorem 2).
1971 ◽
Vol 23
(6)
◽
pp. 1060-1077
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1970 ◽
Vol 22
(4)
◽
pp. 878-880
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2001 ◽
Vol 25
(12)
◽
pp. 757-762
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1965 ◽
Vol 17
◽
pp. 977-1009
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Keyword(s):
1967 ◽
Vol 19
◽
pp. 376-393
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1984 ◽
Vol 96
(1-2)
◽
pp. 95-96
◽
1976 ◽
Vol 41
(2)
◽
pp. 391-404
◽
1957 ◽
Vol 9
◽
pp. 378-388
◽