On $\mathfrak{F_{\mathrm s}}$-Quasinormality of 2-Maximal Subgroups
Received:April 08, 2012  Revised:November 25, 2012
Key Word: $\mathfrak{F_{\mathrm s}}$-quasinormal subgroup   Sylow subgroup   maximal subgroup   $2$-maximal subgroup.  
Fund ProjectL: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).
Author NameAffiliation
Yufeng LIU School of Mathematical and Information Science, Shandong Institute of Business and Technology, Shandong 264005, P. R. China 
Xiaolong YU School of Mathematical Sciences, University of Science and Technology of China, Anhui 230026, P. R. China 
Lijun HUO School of Mathematical Sciences, University of Science and Technology of China, Anhui 230026, P. R. China 
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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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