Let G be a finite group. A subgroup H of G is said to be an <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\mathcal {H}$</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">H</mi> </math></EquationSource> </InlineEquation>-subgroup of G if <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$N_{G}(H)\cap H^{g}\le H$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>N</mi> <mi>G</mi> </msub> <mrow> <mo stretchy="false">(</mo> <mi>H</mi> <mo stretchy="false">)</mo> </mrow> <mo>∩</mo> <msup> <mi>H</mi> <mi>g</mi> </msup> <mo>≤</mo> <mi>H</mi> </mrow> </math></EquationSource> </InlineEquation> for all <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$g\in G$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>g</mi> <mo>∈</mo> <mi>G</mi> </mrow> </math></EquationSource> </InlineEquation>. A subgroup H of G is called weakly c-supplemented in G if there exists a subgroup K of G such that <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$G=HK$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>G</mi> <mo>=</mo> <mi>H</mi> <mi>K</mi> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$H\cap K$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>H</mi> <mo>∩</mo> <mi>K</mi> </mrow> </math></EquationSource> </InlineEquation> is an <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$\mathcal {H}$</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">H</mi> </math></EquationSource> </InlineEquation>-subgroup in G. In this paper, we investigate the structure of a finite group in which some subgroups are weakly c-supplemented in a local subgroup. Our results generalize and improve several known results.

On local weakly c-supplemented subgroups of finite groups

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发表日期：

2026年5月11日

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Songtai Li,
Jianjun Liu

摘要

Let G be a finite group. A subgroup H of G is said to be an $\mathcal {H}$ $H$ -subgroup of G if $N_{G}(H)\cap H^{g}\le H$ $N_{G} (H) \cap H^{g} \leq H$ for all $g\in G$ $g \in G$ . A subgroup H of G is called weakly c-supplemented in G if there exists a subgroup K of G such that $G=HK$ $G = H K$ and $H\cap K$ $H \cap K$ is an $\mathcal {H}$ $H$ -subgroup in G. In this paper, we investigate the structure of a finite group in which some subgroups are weakly c-supplemented in a local subgroup. Our results generalize and improve several known results.