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<p>Let <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\mathcal D\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">D</mi> </math></EquationSource> </InlineEquation> be a nontrivial 2-<InlineEquation ID="IEq5"> <EquationSource Format="TEX">\((v,k,\lambda )\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>v</mi> <mo>,</mo> <mi>k</mi> <mo>,</mo> <mi>λ</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> design, and let <i>G</i> be a flag-transitive block-primitive automorphism group of <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\mathcal D\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">D</mi> </math></EquationSource> </InlineEquation>. In this paper, we determine all such pairs <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\((\mathcal {D},G)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="script">D</mi> <mo>,</mo> <mi>G</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>, where the socle of <i>G</i> is a sporadic simple group.</p>

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Block-primitive 2-\((v,k,\lambda )\) designs with sporadic socle

  • 期刊论文

  • 发表日期：

    2026年2月2日

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  • Suyun Ding,
  • Xiaoqin Zhan

摘要

Let \(\mathcal D\) D be a nontrivial 2- \((v,k,\lambda )\) ( v , k , λ ) design, and let G be a flag-transitive block-primitive automorphism group of \(\mathcal D\) D . In this paper, we determine all such pairs \((\mathcal {D},G)\) ( D , G ) , where the socle of G is a sporadic simple group.