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<p>A subgroup <i>H</i> of a finite group <i>G</i> is called <i>S</i>-semipermutable in <i>G</i> if <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(HQ=QH\)</EquationSource> </InlineEquation> for all Sylow <i>q</i>-subgroups <i>Q</i> of <i>G</i> for all primes <i>q</i> not dividing |<i>H</i>|. In this paper, we study the solvability and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\pi \)</EquationSource> </InlineEquation>-solvability of finite groups in which all non-normal Sylow subgroups of every Schmidt subgroup are <i>S</i>-semipermutable.</p>

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On the solvability of a finite group with some S-semipermutable subgroups

  • 期刊论文

  • 发表日期：

    2026年1月27日

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  • Songtai Li,
  • Tianwei Zheng,
  • Jianjun Liu

摘要

A subgroup H of a finite group G is called S-semipermutable in G if \(HQ=QH\) for all Sylow q-subgroups Q of G for all primes q not dividing |H|. In this paper, we study the solvability and \(\pi \) -solvability of finite groups in which all non-normal Sylow subgroups of every Schmidt subgroup are S-semipermutable.