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On the automorphisms of 2−(v,k,1) designs

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  • Li, Shangzhao
  • Liu, Weijun
  • Li, Xianhua

Abstract

Thirty years ago, a six-person team classified the pairs (D,G) where D is a 2−(v,k,1) design and G is a flag-transitive automorphism group of D, with the exception of those in which G is a one-dimensional affine group. Since then the effort has been to classify those D, designs which are block-transitive but not flag-transitive. This paper contributes to the program for determining the pairs 2−(v,k,1) in which (D,G) has a block-transitive group G of automorphisms. It is clear that if one wishes to study the structure of a finite group acting on a D design then describing the socle is an important first step. Here we prove that if G is a block-transitive group of automorphisms of 2−(v,k,1) which has D as its socle then T is also transitive on the blocks of T=2F4(q).

Suggested Citation

  • Li, Shangzhao & Liu, Weijun & Li, Xianhua, 2017. "On the automorphisms of 2−(v,k,1) designs," Applied Mathematics and Computation, Elsevier, vol. 292(C), pages 120-127.
    • Handle: RePEc:eee:apmaco:v:292:y:2017:i:c:p:120-127
    DOI: 10.1016/j.amc.2016.06.027
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    Cited by:

    1. Li, Shangzhao & Liu, Weijun & Li, Xianhua, 2019. "2−(v,k,1) designs admitting automorphism groups with socle Sz(q)," Applied Mathematics and Computation, Elsevier, vol. 351(C), pages 153-161.
    2. Tang, Jianxiong & Yang, Chaohui & Li, Shangzhao & Dai, Shaojun & Liu, Weijun, 2020. "Block transitive 2−(v,k,1) designs and PGL2(q) groups," Applied Mathematics and Computation, Elsevier, vol. 374(C).
    3. Mohamad, Mostafa & Songthaveephol, Veerasith, 2020. "Clash of titans: The challenges of socio-technical transitions in the electrical vehicle technologies – the case study of Thai automotive industry," Technological Forecasting and Social Change, Elsevier, vol. 153(C).

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