| 徐满红,郭文彬,黄建红.有限群的弱S-拟正规嵌入子群[J].数学年刊A辑,2011,32(3):299~306 |
| 有限群的弱S-拟正规嵌入子群 |
| Finite Groups with Weakly S-Quasinormally Embedded Subgroups |
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| DOI： |
| 中文关键词: 有限群 弱S-拟正规嵌入子群 极小子群 极大子群 群类 |
| 英文关键词:Finite group Weakly 5-quasinormally embedded subgroup Minimal subgroup Maximal subgroup Class of groups |
| 基金项目:国家自然科学基金(No.11071229)资助的项目 |
| Author Name | Affiliation | E-mail | | XU Manhong | School of Mathematical Sciences,Xuzhou Normal University,Xuzhou 221116,Jiangsu,China. | moyan8022@163.com | | GUO Wenbin | School of Mathematical Sciences,China,Department of Mathematics,University of Science and Technology of China,Hefei 230026 | wbguo@ustc.edu.cn | | HUANG Jianhong | Department of Mathematics, University of Science and Technology of China, Hefei 230026, China. | jhh320@126.com |
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| 中文摘要: |
| 群$G$的子群$H$称为在$G$中$S$-拟正规嵌入的, 如果对于任意的素数$p \mid |H|$, $H$的Sylow $p$-子群也是$G$的某个$S$-拟正规子群的Sylow $p$-子群.
称群$G$的子群$H$在$G$中弱$S$-拟正规嵌入, 如果存在群$G$的正规子群$T$,
使得$HT \unlhd G$且$H \cap T$在$G$中是$S$-拟正规嵌入的.
研究了弱$S$-拟正规嵌入子群的性质, 给出了某些群类的新的特征, 并推广了一些已知的结论. |
| 英文摘要: |
| A subgroup $H$ of $G$ is called $S$-quasinormally embedded in $G$ if for each prime $p \mid |H|$,
a Sylow $p$-subgroup of $H$ is also a Sylow $p$-subgroup of some $S$-quasinormal subgroup of $G$.
A subgroup $H$ of $G$ is called weakly $S$-quasinormally embedded
in $G$ if there exists a normal subgroup $T$ of $G$ such that $HT \unlhd G$ and
$H \cap T$ is $S$-quasinormally embedded in $G$.
The properties of weakly $S$-quasinormally embedded subgroups are obtained. The new characterizations of some classes of
finite groups are given and some previously known results are generalized. |
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