| 李世荣,杜妮,钟祥贵.有限群的素数幂阶S-拟正规嵌入子群[J].数学年刊A辑,2011,32(1):27~32 |
| 有限群的素数幂阶S-拟正规嵌入子群 |
| On S-Quasinormally Embedded Subgroups of Prime Power Order in Finite Groups |
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| DOI： |
| 中文关键词: 饱和群系 S-拟正规嵌入子群 |
| 英文关键词:Saturated formation S-quasinormally embedded subgroup |
| 基金项目:国家自然科学基金(No.0249001,No.10961007); 中央高校基本科研业务费专项资金(No.2010121003); 广西省自然科学基金(No.0575050)资助的项目 |
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| 中文摘要: |
| 设$G$ 为有限
$p$-可解群, 其中$p$ 为$|G|$的奇素因子.
若$P$ 为$G$的Sylow $p$-子群且最小生成系含 $d$个元素.考虑集合${\cal M}_d(P)=\{P_1,\cdots,P_d\}$,其中$P_1,\cdots,P_d$是$P$的极大子群且满足bigcap\limits_{i=1}^d P_i=\Phi (P)$. 证明了若 ${\cal M}_d(P)$中每个元在$G$中是$S$-拟正规嵌入的, 则 $G$ 为$p$-超可解群.作为应用,还得到了一些进一步的结论. |
| 英文摘要: |
| $p$-solvable finite group, where $p$ is an odd prime divisor of $|G|$,
and $P$ be a Sylow $p$-subgroup of $G$ with the smallest generator number $d$.
Consider the set ${\cal M}_d(P)=\{P_1,\cdots,P_d\}$, where $P_1,\cdots,P_d$ are the
maximal subgroups of $P$ such that $\bigcap\limits_{i=1}^d P_i=\Phi (P)$.
It is shown that if every member of ${\cal M}_d(P)$
is
$S$-quasinormally embedded in $G$, then $G$ is $p$-supersolvable.
As its applications, some further results are obtained. |
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