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<p>In this paper, we introduce a condition on a subgroup of a finite group that is more general than the concept of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(IC_{p}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>I</mi> <msub> <mi>C</mi> <mi>p</mi> </msub> </mrow> </math></EquationSource> </InlineEquation>-subgroups, and obtain some sufficient and necessary conditions for <i>p</i>-solvability of a finite group.&#xa0;Our results generalize some main theorems of Gao and Lei (Comm. Algebra 52(12): 4987–4991, 2024), and Zhang et al. (Ric. Mat. 2025).</p>

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Some sufficient and necessary conditions for p-solvability of a finite group

  • 期刊论文

  • 发表日期：

    2026年3月16日

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  • Shuo Guo,
  • Haoran Yu,
  • Jian Sun

摘要

In this paper, we introduce a condition on a subgroup of a finite group that is more general than the concept of \(IC_{p}\) I C p -subgroups, and obtain some sufficient and necessary conditions for p-solvability of a finite group. Our results generalize some main theorems of Gao and Lei (Comm. Algebra 52(12): 4987–4991, 2024), and Zhang et al. (Ric. Mat. 2025).