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A common characterization of finite projective spaces and affine planes

par Delandtsheer, Anne ;Beutelspacher, A.
Référence European journal of combinatorics, 2, page (213-219)
Publication Publié, 1981

Article révisé par les pairs

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Résumé :

Let S be a finite linear space for which there is a non-negative integer s such that for any two disjoint lines L, L' of S and any point p outside L and L' there are exactly s lines through p intersecting the two lines L and L'. We prove that one of the following possibilities occurs: S is a generalized projective space, and if the dimension of S is at least 4, then any line of S has exactly two points. S is an affine plane, an affine plane with one improper point, or a punctured projective plane. S is the Fano-quasi -plane. © 1981, Academic Press Inc. (London) Limited. All rights reserved.