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<p>Let <i>A</i> and <i>G</i> be finite groups such that <i>A</i> acts coprimely on <i>G</i> via automorphisms. A subgroup <i>H</i> of <i>G</i> is said to satisfy the <i>IC</i>-property if the intersection of <i>H</i> and [<i>H</i>,&#xa0;<i>G</i>] meets certain specified conditions. In this paper, we investigate the structure of the finite group <i>G</i> under the assumption that certain maximal <i>A</i>-invariant subgroups of <i>G</i> possess the <i>IC</i>-property and obtain some new results in the coprime action setting.</p>

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A note on an IC-property of subgroups of a finite group

  • 期刊论文

  • 发表日期：

    2025年11月6日

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  • Boru Zhang,
  • Qihong Bao,
  • Xiaoxiang Zhao,
  • Xuan Li

摘要

Let A and G be finite groups such that A acts coprimely on G via automorphisms. A subgroup H of G is said to satisfy the IC-property if the intersection of H and [H, G] meets certain specified conditions. In this paper, we investigate the structure of the finite group G under the assumption that certain maximal A-invariant subgroups of G possess the IC-property and obtain some new results in the coprime action setting.