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On a Result of Cameron and Praeger on Block-transitive Point-imprimitive t-designs

In: Algebraic Combinatorics and Applications

Author

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  • Michel Sebille

    (Université Libre de Bruxelles, Département de Mathématiques Campus Plaine C.P. 216)

Abstract

In 1993, Cameron and Praeger proved that if G is a block-transitive point-imprimitive automorphism group of an Sλ (t, k, c2) where c =( 2 k ) − 1, k > 5, k ≠ 8, t >1, then there are two simple 2-transitive permutation groups T1 and T 2 of degree c such that one of the following holds: (i) G is a subgroup of the wreath product Aut(T1) ≀ Sc containing T 1 c and G projects onto a 2-transitive subgroup of Sc, (ii) T1 × T2 ≤ G ≤ Aut(T1) × Aut(T2). Moreover, if (i) or (ii) holds then G acts in this way on such a design. The purpose of this paper is to construct explicit extra-examples showing that this theorem is no longer valid for k ≤ 5 and for k = 8.

Suggested Citation

  • Michel Sebille, 2001. "On a Result of Cameron and Praeger on Block-transitive Point-imprimitive t-designs," Springer Books, in: Anton Betten & Axel Kohnert & Reinhard Laue & Alfred Wassermann (ed.), Algebraic Combinatorics and Applications, pages 316-323, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-59448-9_21
    DOI: 10.1007/978-3-642-59448-9_21
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