| 关于有限群的S-半置换子群 |
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| 引用本文： | 卢家宽,李世荣.关于有限群的S-半置换子群[J].数学研究与评论,2009,29(6):985-991. |
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| 作者姓名： | 卢家宽 李世荣 |
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| 作者单位： | 上海大学数学系, 上海 200444;广西大学数学与信息科学学院, 广西 南宁 530004 |
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| 基金项目： | 国家自然科学基金(No.10471039);广西自然科学基金(No.0249001);上海大学研究生创新基金(No.SHUCX091043). |
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| 摘 要： | Let d be the smallest generator number of a finite p-group P and let Md（P） = {P1,...,Pd} be a set of maximal subgroups of P such that ∩di=1 Pi = Φ（P）. In this paper, we study the structure of a finite group G under the assumption that every member in Md（Gp） is S-semipermutable in G for each prime divisor p of ｜G｜ and a Sylow p-subgroup Gp of G.
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| 关 键 词： | 有限群 子群 置换 Sylow 糖蛋白G 发电机 素因子 子集 |
| 收稿时间： | 2008/1/17 0:00:00 |
| 修稿时间： | 2008/10/16 0:00:00 |
On $S$-Semipermutable Subgroups of Finite Groups |
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| LU Jia Kuan and LI Shi Rong.On $S$-Semipermutable Subgroups of Finite Groups[J].Journal of Mathematical Research and Exposition,2009,29(6):985-991. |
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| Authors: | LU Jia Kuan and LI Shi Rong |
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| Institution: | Department of Mathematics, Shanghai University, Shanghai 200444, China;Department of Mathematics, Guangxi University, Guangxi 530004, China |
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| Abstract: | Let $d$ be the smallest generator number of a finite $p$-group $P$ and let ${\cal M}_d (P)=\{P_{1}, \ldots, P_{d} \}$ be a set of maximal subgroups of $P$ such that $\bigcap _{i=1}^{d}P_{i}=\Phi(P)$. In this paper, we study the structure of a finite group $G$ under the assumption that every member in ${\cal M}_{d}(G_{p})$ is $S$-semipermutable in $G$ for each prime divisor $p$ of $|G|$ and a Sylow $p$-subgroup $G_{p}$ of $G$. |
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| Keywords: | $S$-semipermutable subgroups $p$-nilpotent groups supersolvable groups |
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