On some incidence structures |
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Authors: | Laura Bertani |
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Institution: | 1. Istituto di Matematica, Via Università 12, I-43100, Parma
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Abstract: | In this paper,suggested by André's papers (2), 3]), we construct geometrical structures (X,?,//}) where X is a finite set of points, ? is a set of lines, and // is an equivalence relation on ?. These constructions are made starting with a finite and not empty set X and a permutation group G which is 2-transitive on X and such that the stabilizer of two distinct points of X is different from the identical subgroup. We look for conditions such that the structure (X, ?) is a (3,q)-Steiner system. We remember that a (3,q)-Steiner system is a pair (X,B), where X is a set of elements (called points), B is a system of subsets of X (called blocks), such that: - every block contains q points exactly;
- given three distinct points x,y,z of X, there is exactly one subset of X belonging to B and containing x,y,z.
At the end we construct such a system with the help of a nearskewfield (according to Zassenhaus 7], 8]). |
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