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<p>Finite projective planes are constructed using groups that satisfy simple-looking conditions. The resulting projective planes include many known planes and possibly new ones, and are precisely those having a collineation group fixing a flag <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\((\infty ,L_ \infty )\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>∞</mi> <mo>,</mo> <msub> <mi>L</mi> <mi>∞</mi> </msub> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> and transitive on the flags (<i>w</i>,&#xa0;<i>W</i>) with <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(w\notin L_ \infty \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>w</mi> <mo>∉</mo> <msub> <mi>L</mi> <mi>∞</mi> </msub> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\infty \notin W\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>∞</mi> <mo>∉</mo> <mi>W</mi> </mrow> </math></EquationSource> </InlineEquation>.</p>

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Soft planes and groups

  • 期刊论文

  • 发表日期：

    2026年8月4日

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  • William M. Kantor

摘要

Finite projective planes are constructed using groups that satisfy simple-looking conditions. The resulting projective planes include many known planes and possibly new ones, and are precisely those having a collineation group fixing a flag \((\infty ,L_ \infty )\) ( ∞ , L ∞ ) and transitive on the flags (w, W) with \(w\notin L_ \infty \) w ∉ L ∞ and \(\infty \notin W\) ∞ ∉ W .