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<p>A famous result of P. Hegedűs describes the structure of finite rational <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\{2,5\}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">{</mo> <mn>2</mn> <mo>,</mo> <mn>5</mn> <mo stretchy="false">}</mo> </mrow> </math></EquationSource> </InlineEquation>-groups. In this paper, we show how Hegedűs’ proof can be used to obtain a similar result for the more general situation of a finite rational 2-group acting faithfully and with the eigenvector property on a f.d <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathbb {F}_p\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="double-struck">F</mi> <mi>p</mi> </msub> </math></EquationSource> </InlineEquation>-vector space, where <i>p</i> is a prime with <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(p\ge 5\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>p</mi> <mo>≥</mo> <mn>5</mn> </mrow> </math></EquationSource> </InlineEquation>.</p>

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A Generalization of a Result of Hegedűs

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月9日

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  • Sara C. Debón

摘要

A famous result of P. Hegedűs describes the structure of finite rational \(\{2,5\}\) { 2 , 5 } -groups. In this paper, we show how Hegedűs’ proof can be used to obtain a similar result for the more general situation of a finite rational 2-group acting faithfully and with the eigenvector property on a f.d \(\mathbb {F}_p\) F p -vector space, where p is a prime with \(p\ge 5\) p ≥ 5 .