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<p>It is clear that the automorphism group of the (15,&#xa0;8,&#xa0;4)-design of points and hyperplane complements of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\({{\,\textrm{PG}\,}}(3,2)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mrow> <mspace width="0.166667em" /> <mtext>PG</mtext> <mspace width="0.166667em" /> </mrow> <mo stretchy="false">(</mo> <mn>3</mn> <mo>,</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> is <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\({{\,\textrm{GL}\,}}(4,2)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mrow> <mspace width="0.166667em" /> <mtext>GL</mtext> <mspace width="0.166667em" /> </mrow> <mo stretchy="false">(</mo> <mn>4</mn> <mo>,</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>. Using methods of point-line geometries, we determine the automorphism groups of the remaining four symmetric (15,&#xa0;8,&#xa0;4)-designs and describe their actions on the sets of points and blocks.</p>

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The automorphism groups of the five symmetric (15, 8, 4)-designs

  • 期刊论文

  • 发表日期：

    2026年5月15日

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  • Mark Pankov,
  • Krzysztof Petelczyc,
  • Mariusz Żynel

摘要

It is clear that the automorphism group of the (15, 8, 4)-design of points and hyperplane complements of \({{\,\textrm{PG}\,}}(3,2)\) PG ( 3 , 2 ) is \({{\,\textrm{GL}\,}}(4,2)\) GL ( 4 , 2 ) . Using methods of point-line geometries, we determine the automorphism groups of the remaining four symmetric (15, 8, 4)-designs and describe their actions on the sets of points and blocks.