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<p>Let <i>G</i> be a finite group. A subgroup <i>H</i> of <i>G</i> is called weakly nearly <i>S</i>-permutable in <i>G</i> if there exists a normal subgroup <i>K</i> of <i>G</i> such that <i>G</i> = <i>HK</i> and <i>H</i> ∩ <i>K</i> is nearly <i>S</i>-permutable in <i>G</i>. We investigate the influence of primary weakly nearly <i>S</i>-permutable subgroups on the structure of group <i>G</i>. In particular, some new criteria for a group to be <i>p</i>-nilpotent or supersoluble are given.</p>

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Structure of finite groups decided by the property of primary subgroups

  • 期刊论文

  • 发表日期：

    2026年3月23日

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  • Ruifang Chen,
  • Chen Wang,
  • Xianhe Zhao

摘要

Let G be a finite group. A subgroup H of G is called weakly nearly S-permutable in G if there exists a normal subgroup K of G such that G = HK and H ∩ K is nearly S-permutable in G. We investigate the influence of primary weakly nearly S-permutable subgroups on the structure of group G. In particular, some new criteria for a group to be p-nilpotent or supersoluble are given.