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<p>In 2022, C. Fiori presented a construction of an infinite family of finite sharply 3-transitive permutation sets. However, her setting contains an essential flaw so that only the known finite sharply 3-transitive permutation sets arise. We use the underlying principle of this process and a construction of hyperbola structures over half-ordered fields to generalize the methods to obtain infinite sharply 3-transitive sets of permutations on the projective lines over fields for which the subgroup of nonzero squares has index <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(&gt;2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>&gt;</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation> in the multiplicative group of the field.</p>

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A New Construction of Infinite Sharply 3-Transitive Permutation Sets

  • 期刊论文

  • 发表日期：

    2026年3月2日

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  • Günter F. Steinke

摘要

In 2022, C. Fiori presented a construction of an infinite family of finite sharply 3-transitive permutation sets. However, her setting contains an essential flaw so that only the known finite sharply 3-transitive permutation sets arise. We use the underlying principle of this process and a construction of hyperbola structures over half-ordered fields to generalize the methods to obtain infinite sharply 3-transitive sets of permutations on the projective lines over fields for which the subgroup of nonzero squares has index \(>2\) > 2 in the multiplicative group of the field.