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<p>Let <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11202_2025_1588_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">$ \sigma $</EquationSource> </InlineEquation> be a partition of the set of all primes.A finite group <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11202_2025_1588_Article_IEq3.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">$ G $</EquationSource> </InlineEquation> is said to be <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11202_2025_1588_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">$ \sigma $</EquationSource> </InlineEquation>-supersolvable if every <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11202_2025_1588_Article_IEq3.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">$ G $</EquationSource> </InlineEquation>-chief factor of its <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11202_2025_1588_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">$ \sigma $</EquationSource> </InlineEquation>-nilpotent residual is cyclic.This paper studies the structure of minimal non-<InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11202_2025_1588_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">$ \sigma $</EquationSource> </InlineEquation>-supersolvable groups that are not <InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11202_2025_1588_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">$ \sigma $</EquationSource> </InlineEquation>-solvable.</p>

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Finite Minimal Non-\( \sigma \)-Supersolvable Groups

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  • 发表日期：

    2025年7月23日

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  • O. L. Shemetkova

摘要

Let $ \sigma $ be a partition of the set of all primes.A finite group $ G $ is said to be $ \sigma $ -supersolvable if every $ G $ -chief factor of its $ \sigma $ -nilpotent residual is cyclic.This paper studies the structure of minimal non- $ \sigma $ -supersolvable groups that are not $ \sigma $ -solvable.