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<p>The purpose of this paper is to contribute part of the classification of nontrivial 2-design <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathcal {D}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">D</mi> </math></EquationSource> </InlineEquation> with prime length of blocks admitting a flag-transitive and point-primitive automorphism group <i>G</i> of almost simple type whose socle <i>X</i> is a projective special linear group of dimension at least 3. We prove that such a design belongs to an infinite families of projective spaces or it is isomorphic to a design with parameters (8,&#xa0;56,&#xa0;21,&#xa0;3,&#xa0;6) or (8,&#xa0;56,&#xa0;35,&#xa0;5,&#xa0;20).</p>

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On flag-transitive 2-designs with prime block length and projective special linear groups

  • 期刊论文

  • 发表日期：

    2026年1月5日

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  • Mohsen Bayat,
  • Nasrin Soltankhah

摘要

The purpose of this paper is to contribute part of the classification of nontrivial 2-design \(\mathcal {D}\) D with prime length of blocks admitting a flag-transitive and point-primitive automorphism group G of almost simple type whose socle X is a projective special linear group of dimension at least 3. We prove that such a design belongs to an infinite families of projective spaces or it is isomorphic to a design with parameters (8, 56, 21, 3, 6) or (8, 56, 35, 5, 20).