| On $CAP$-Embedded Subgroups in Finite Groups |
| Received:September 20, 2007 Revised:January 04, 2008 |
| Key Words:
$CAP$-embedded subgroups maximal subgroups $p$-nilpotent groups supersolvable groups.
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| Fund Project:the National Natural Science Foundation of China (No.10771132); Jiangsu ``Qing-lan Project'' for Excellent Young Teachers in University (2006). |
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| Abstract: |
| A subgroup $H$ of a finite group $G$ is said to be $CAP$-embedded subgroup of $G$ if, for each prime $p$ dividing the order of $H$, there exists a $CAP$-subgroup $K$ of $G$ such that a Sylow $p$-subgroup of $H$ is also a Sylow $p$-subgroup of $K$. In this paper some new results are obtained based on the assumption that some subgroups of prime power order have the $CAP$-embedded property in the group. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2009.06.007 |
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