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<p>Let <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="373_2025_2956_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="82" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathcal {D}=(\mathcal {P},\mathcal {B})\)</EquationSource> </InlineEquation> be a 2-(45,&#xa0;12,&#xa0;8) design with a flag-transitive automorphism group <i>G</i>. This paper aims to give a characterization of <i>G</i>. As a conclusion, we get that <i>G</i> acts imprimitively on <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="373_2025_2956_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathcal {P}\)</EquationSource> </InlineEquation> if and only if the Fitting subgroup of <i>G</i> acts regularly on <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="373_2025_2956_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathcal {P}\)</EquationSource> </InlineEquation>.</p>

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Flag-Transitive 2-(45, 12, 8) Designs

  • 期刊论文

  • 发表日期：

    2025年8月6日

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  • Yajie Wang,
  • Zhilin Zhang,
  • Shenglin Zhou

摘要

Let \(\mathcal {D}=(\mathcal {P},\mathcal {B})\) be a 2-(45, 12, 8) design with a flag-transitive automorphism group G. This paper aims to give a characterization of G. As a conclusion, we get that G acts imprimitively on \(\mathcal {P}\) if and only if the Fitting subgroup of G acts regularly on \(\mathcal {P}\) .