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arXiv · 1408.6598

Constructing flag-transitive, point-imprimitive designs

Peter J. Cameron·Cheryl E. Praeger
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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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Peter J. Cameron, Cheryl E. Praeger. 2014-08-28. Constructing flag-transitive, point-imprimitive designs. https://arxiv.org/abs/1408.6598

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