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<p>We construct infinite series of subgroup <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11202_2025_1536_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">$ m $</EquationSource> </InlineEquation>-functors and regular subgroup<InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11202_2025_1536_Article_IEq2.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">$ m $</EquationSource> </InlineEquation>-functors <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11202_2025_1536_Article_IEq3.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">$ \theta $</EquationSource> </InlineEquation> such that the Frattini <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11202_2025_1536_Article_IEq4.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">$ \theta $</EquationSource> </InlineEquation>-subgroup ofevery normal Hall subgroup <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11202_2025_1536_Article_IEq5.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">$ H $</EquationSource> </InlineEquation> in any finite group <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11202_2025_1536_Article_IEq6.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">$ G $</EquationSource> </InlineEquation> is equal to theintersection of <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11202_2025_1536_Article_IEq7.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">$ H $</EquationSource> </InlineEquation> with the Frattini <InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11202_2025_1536_Article_IEq8.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">$ \theta $</EquationSource> </InlineEquation>-subgroup of <InlineEquation ID="IEq9"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11202_2025_1536_Article_IEq9.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">$ G $</EquationSource> </InlineEquation>.</p>

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On One Property of Normal Hall Subgroups of Finite Groups

  • 期刊论文

  • 发表日期：

    2025年3月23日

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  • X. Yi,
  • B. Cheng,
  • R. V. Borodich,
  • S. F. Kamornikov

摘要

We construct infinite series of subgroup $ m $ -functors and regular subgroup $ m $ -functors $ \theta $ such that the Frattini $ \theta $ -subgroup ofevery normal Hall subgroup $ H $ in any finite group $ G $ is equal to theintersection of $ H $ with the Frattini $ \theta $ -subgroup of $ G $ .