Groupes de permutations primitifs d'ordre impair et denombrement de tournois sommet-primitifs |
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Authors: | Annie Astie |
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Affiliation: | Laboratoire de Statistique, Université Paul Sabatier, Toulouse, France |
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Abstract: | A tournament T (directed graph in which there is exactly one arc between any two vertices) is said to be point-primitive if its automorphism group A(T) acts primitively on the vertices of T. Automorphism groups of point-primitive tournaments are primitive permutation groups of odd order, which are known to be affine groups; and so point-primitive tournaments are of prime-power order. Some properties of primitive permutation groups of odd order are proved and a counting formula for point-primitive tournaments of order p2k (p prime number, k integer ?0) is derived from them. |
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