Dimensional linear spaces whose automorphism group is (line,hyperplane)-flag transitive |
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Authors: | Anne Delandtsheer |
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Affiliation: | (1) U.L.B., cp. 214, Boulevard du Triomphe, B-1050 Brussels, Belgium |
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Abstract: | We classify the pairs (S, G) where S is a finite n-dimensional linear space with n 4 and G is an automorphism group of S acting transitively on the (line, hyperplane)-flags. We show in particular that S must be either a Desarguesian projective or affine space provided with its subspaces of dimension n - 1, or a Mathieu-Witt design provided with its blocks and its subsets of size n - 1. Our proof uses a recent classification of the flag transitive 2-(v, k, 1) designs, which in turn heavily depends on the classification of all finite simple groups. The case n = 3 has been settled in another paper. |
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