Geodesic
On $\Pi $-property of some maximal subgroups of Sylow subgroups of finite groups
Czechoslovak Mathematical Journal, Tome 73 (2023) no. 4, pp. 1349-1358
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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 study the influence of some $p$-subgroups of $G$ satisfying the $\Pi $-property on the structure of $G$, and generalize some known results.
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 study the influence of some $p$-subgroups of $G$ satisfying the $\Pi $-property on the structure of $G$, and generalize some known results.
DOI : 10.21136/CMJ.2023.0089-23
Classification : 20D10, 20D20
Keywords: finite group; $p$-supersoluble group, $p$-nilpotent group, $\Pi $-property 
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     author = {Qiu, Zhengtian and Liu, Jianjun and Chen, Guiyun},
     title = {On $\Pi $-property of some maximal subgroups of {Sylow} subgroups of finite groups},
     journal = {Czechoslovak Mathematical Journal},
     pages = {1349--1358},
     year = {2023},
     volume = {73},
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Qiu, Zhengtian; Liu, Jianjun; Chen, Guiyun. On $\Pi $-property of some maximal subgroups of Sylow subgroups of finite groups. Czechoslovak Mathematical Journal, Tome 73 (2023) no. 4, pp. 1349-1358. doi: 10.21136/CMJ.2023.0089-23

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