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Constructing flag-transitive, point-imprimitive designs

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Abstract

We give a construction of a family of designs with a specified point-partition and determine the subgroup of automorphisms leaving invariant the point-partition. We give necessary and sufficient conditions for a design in the family to possess a flag-transitive group of automorphisms preserving the specified point-partition. We give examples of flag-transitive designs in the family, including a new symmetric 2-(1408,336,80) design with automorphism group \(2^{12}:((3\cdot \mathrm {M}_{22}):2)\) and a construction of one of the families of the symplectic designs (the designs \(S^-(n)\)) exhibiting a flag-transitive, point-imprimitive automorphism group.

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Authors and Affiliations

  1. Mathematical Institute, University of St Andrews, North Haugh, St Andrews, Fife, UK

    Peter J. Cameron

  2. School of Mathematics and Statistics, University of Western Australia, Crawley, WA, 6009, Australia

    Cheryl E. Praeger

Authors
  1. Peter J. Cameron
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  2. Cheryl E. Praeger
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Correspondence to Peter J. Cameron.

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Cameron, P.J., Praeger, C.E. Constructing flag-transitive, point-imprimitive designs. J Algebr Comb 43, 755–769 (2016). https://doi.org/10.1007/s10801-015-0591-4

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  • DOI: https://doi.org/10.1007/s10801-015-0591-4

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