| 2-极大子群的$F_s$-拟正规性 |
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| 引用本文： | 刘玉凤,余小龙,霍利军.2-极大子群的$F_s$-拟正规性[J].数学研究及应用,2013,33(4):412-418. |
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| 作者姓名： | 刘玉凤 余小龙 霍利军 |
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| 作者单位： | 山东工商学院数学与信息科学学院, 山东 烟台 264005;中国科学技术大学数学科学学院, 安徽 合肥 230026;中国科学技术大学数学科学学院, 安徽 合肥 230026 |
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| 基金项目： | 国家自然科学基金(Grant No.11071147),国家高校博士项目基金(Grant No.20113402110036). |
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| 摘 要： | $F$是一个群系. $G$的子群$H$在$G$中称为$F_s$-拟正规的,如果存在$G$的正规子群$T$,使得$HT$在$G$中是$s$-置换的并且$(H\cap T)H_G/H_G$包含在$G/H_G$的$F$超中心$Z^F_\infty(G/H_G)$中.本文利用$F_s$-拟正规子群研究了有限群的结构.获得了某些新的结果.
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| 关 键 词： | $F_s$-拟正规子群 Sylow子群 极大子群 2-极大子群. |
| 收稿时间： | 4/8/2012 12:00:00 AM |
| 修稿时间： | 2012/11/25 0:00:00 |
On $\mathfrak{F_{\mathrm s}}$-Quasinormality of 2-Maximal Subgroups |
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| Yufeng LIU,Xiaolong YU and Lijun HUO.On $\mathfrak{F_{\mathrm s}}$-Quasinormality of 2-Maximal Subgroups[J].Journal of Mathematical Research with Applications,2013,33(4):412-418. |
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| Authors: | Yufeng LIU Xiaolong YU and Lijun HUO |
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| Institution: | School of Mathematical and Information Science, Shandong Institute of Business and Technology, Shandong 264005, P. R. China;School of Mathematical Sciences, University of Science and Technology of China, Anhui 230026, P. R. China;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. |
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| Keywords: | $\mathfrak{F_{\mathrm s}}$-quasinormal subgroup Sylow subgroup maximal subgroup $2$-maximal subgroup |
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