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Flag-transitive 4-(v, k, 3) designs and PSL(2, q) groups

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  • Dai, Shaojun
  • Li, Shangzhao

Abstract

Among the properties of homogeneity of incidence structures, flag-transitivity obviously is a particularly important and natural one. Originally, Buekenhout et al. reached a classification of flag-transitive Steiner 2-designs. Recently, Huber completely classified all flag-transitive Steiner t-designs with t ≤ 6 using the classification of the finite 2-transitive permutation groups. Hence the determination of all flag-transitive t-designs with λ ≥ 2 has remained of particular interest and has been known as a long-standing and still open problem.This article is a contribution to the study of the automorphism groups of 4-(v, k, 3) designs. Let S=(P,B) be a non-trivial 4-(q+1,k,3) design. If PSL(2, q) acts flag-transitively on S, then S is a 4-(168,12,3) design and GB is conjugate to A4 or Z12.

Suggested Citation

  • Dai, Shaojun & Li, Shangzhao, 2018. "Flag-transitive 4-(v, k, 3) designs and PSL(2, q) groups," Applied Mathematics and Computation, Elsevier, vol. 332(C), pages 167-171.
    • Handle: RePEc:eee:apmaco:v:332:y:2018:i:c:p:167-171
    DOI: 10.1016/j.amc.2018.03.012
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    Keywords

    Flag-transitive; t-design; PSL(2; q);
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