| On $\mathfrak{F_{\mathrm s}}$-Quasinormality of 2-Maximal Subgroups |
| Received:April 08, 2012 Revised:November 25, 2012 |
| Key Words:
$\mathfrak{F_{\mathrm s}}$-quasinormal subgroup Sylow subgroup maximal subgroup $2$-maximal subgroup.
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant No.11071147) and Doctoral Program Foundation of Institutions of Higher Education of China (Grant No.20113402110036). |
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| Abstract: |
| Let $\frak{F}$ be a class of finite groups. A subgroup $H$ of a finite group $G$ is said to be $\mathfrak{F_{\mathrm s}}$-quasinormal in $G$ if there exists a normal subgroup $T$ of $G$ such that $HT$ is $s$-permutable in $G$ and $(H\cap T)H_G/H_G$ is contained in the $\frak{F}$-hypercenter $Z_\infty ^\frak{F} (G/H_G)$ of $G/H_G$. In this paper, we use $\mathfrak{F_{\mathrm s}}$-quasinormal subgroups to study the structure of finite groups. Some new results are obtained. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2013.04.004 |
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