Geodesic
Finite Projective Planes with Affine Subplanes
Canadian mathematical bulletin, Tome 7 (1964) no. 4, pp. 549-559

Voir la notice de l'article provenant de la source Cambridge University Press

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). 
Ostrom, T. G.; Sherk, F. A. Finite Projective Planes with Affine Subplanes. Canadian mathematical bulletin, Tome 7 (1964) no. 4, pp. 549-559. doi: 10.4153/CMB-1964-051-8
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[4] 4. Hall, Marshall Jr., The Theory of Groups, New York, 1959. Google Scholar

[5] 5. Neumann, Hanna, On Some Finite Non-Desarguesian Planes, Archiv der Mathematik, VI, 1955, pp. 36–40. Google Scholar

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