Let G be a finite group and H a subgroup of G. Suppose that p is a fixed prime dividing the order of G. We call H is <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$c^{}_p$</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mi>c</mi> <mi>p</mi> <mrow> <mrow /> <mo>∗</mo> </mrow> </mmultiscripts> </math></EquationSource> </InlineEquation>-normal in G if there exists a normal subgroup T of G containing <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$H_G$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>H</mi> <mi>G</mi> </msub> </math></EquationSource> </InlineEquation> such that <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$G = HT$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>G</mi> <mo>=</mo> <mi>H</mi> <mi>T</mi> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$|(H\cap T)/H_G|_p\le p$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mrow> <mo stretchy="false">|</mo> <mrow> <mo stretchy="false">(</mo> <mi>H</mi> <mo>∩</mo> <mi>T</mi> <mo stretchy="false">)</mo> </mrow> <mo stretchy="false">/</mo> </mrow> <msub> <mi>H</mi> <mi>G</mi> </msub> <msub> <mrow> <mo stretchy="false">|</mo> </mrow> <mi>p</mi> </msub> <mo>≤</mo> <mi>p</mi> </mrow> </math></EquationSource> </InlineEquation>. In this paper, we provide several characterizations of a group G in which certain classes of subgroups are <InlineEquation ID="IEq8"> <EquationSource Format="TEX">$c_p^$</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi>c</mi> <mi>p</mi> <mo>∗</mo> </msubsup> </math></EquationSource> </InlineEquation>-normal in G. Many known results are extended.

On $c^{*}_p$-normal subgroups of finite groups

期刊论文
发表日期：

2025年11月24日

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Yubo Lv,
Yangming Li,
Xiaoxia Dong

摘要

Let G be a finite group and H a subgroup of G. Suppose that p is a fixed prime dividing the order of G. We call H is $c^{*}_p$ $c_{p}^{*}$ -normal in G if there exists a normal subgroup T of G containing $H_G$ $H_{G}$ such that $G = HT$ $G = H T$ and $|(H\cap T)/H_G|_p\le p$ $| (H \cap T) / H_{G} |_{p} \leq p$ . In this paper, we provide several characterizations of a group G in which certain classes of subgroups are $c_p^*$ $c_{p}^{*}$ -normal in G. Many known results are extended.

On \(c^{*}_p\)-normal subgroups of finite groups

摘要