Geodesic
A note on the $\Pi $-property of some subgroups of finite groups
Czechoslovak Mathematical Journal, Tome 74 (2024) no. 3, pp. 943-953
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Let $H$ be a subgroup of a finite group $G$. We say that $H$ satisfies the $\Pi $-property in $G$ if for any chief factor $L / K$ of $G$, $ |G/K : N_{G/K}(HK/K\cap L/K )| $ is a $\pi (HK/K\cap L/K)$-number. We obtain some criteria for the $p$-supersolubility or $p$-nilpotency of a finite group and extend some known results by concerning some subgroups that satisfy the $\Pi $-property.
Let $H$ be a subgroup of a finite group $G$. We say that $H$ satisfies the $\Pi $-property in $G$ if for any chief factor $L / K$ of $G$, $ |G/K : N_{G/K}(HK/K\cap L/K )| $ is a $\pi (HK/K\cap L/K)$-number. We obtain some criteria for the $p$-supersolubility or $p$-nilpotency of a finite group and extend some known results by concerning some subgroups that satisfy the $\Pi $-property.
DOI : 10.21136/CMJ.2024.0226-24
Classification : 20D10, 20D20
Keywords: finite group; $p$-supersoluble group; $p$-nilpotent group; the $\Pi $-property 
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     title = {A note on the $\Pi $-property of some subgroups of finite groups},
     journal = {Czechoslovak Mathematical Journal},
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     year = {2024},
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Qiu, Zhengtian; Chen, Guiyun; Liu, Jianjun. A note on the $\Pi $-property of some subgroups of finite groups. Czechoslovak Mathematical Journal, Tome 74 (2024) no. 3, pp. 943-953. doi: 10.21136/CMJ.2024.0226-24

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