| On $S$-Semipermutable Subgroups of Finite Groups |
| Received:January 17, 2008 Revised:October 16, 2008 |
| Key Words:
$S$-semipermutable subgroups $p$-nilpotent groups supersolvable groups.
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| Fund Project:the National Natural Science Foundation of China (No.10161001); the Natural Science Foundation of Guangxi Autonomous Region (No.0249001); a Research Grant of Shanghai University (No.SHUCX091043). |
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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 $G$. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2009.06.006 |
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