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

  • Michel Sebille
Conference paper


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:
  1. (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,

  2. (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The purpose of this paper is to construct explicit extra-examples showing that this theorem is no longer valid for k ≤ 5 and for k = 8.


Automorphism Group Discrete Math Permutation Group Wreath Product Transitive Group 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Michel Sebille
    • 1
  1. 1.Département de Mathématiques Campus Plaine C.P. 216Université Libre de BruxellesBruxellesBelgium

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