Constructing flag-transitive, point-imprimitive designs

Peter Jephson Cameron; Cheryl E. Praeger

doi:10.1007/s10801-015-0591-4

Constructing flag-transitive, point-imprimitive designs

Peter Jephson Cameron, Cheryl E. Praeger

Research output: Contribution to journal › Article › peer-review

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⋅M22):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.

Original language	English
Pages (from-to)	755-769
Journal	Journal of Algebraic Combinatorics
Volume	43
Issue number	4
Early online date	2 Apr 2015
DOIs	https://doi.org/10.1007/s10801-015-0591-4
Publication status	Published - 4 May 2016

Keywords

Flag-transitive design
Point-imprimitive
Automorphism group

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10.1007/s10801-015-0591-4

flagtrans_revised_v3
© Springer Science+Business Media New York 2015. The final publication is available at Springer via http://dx.doi.org/10.1007/s10801-015-0591-4
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Cite this

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AB - 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⋅M22):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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KW - Automorphism group

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Constructing flag-transitive, point-imprimitive designs

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Keywords

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