| X-s-Permutable Subgroups |
| Received:November 13, 2007 Revised:March 08, 2008 |
| Key Words:
finite groups formations $X$-$s$-permutable subgroups Sylow subgroups maximal subgroups.
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| Fund Project:the National Natural Science Foundation of China (No.10771180); the Postgraduate Innovation Grant of Jiangsu Province and the International Joint Research Fund between NSFC and RFBR. |
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| Abstract: |
| Let $X$ be a nonempty subset of a group $G$. A subgroup $H$ of $G$ is said to be $X$-$s$-permutable in $G$ if, for every Sylow subgroup $T$ of $G$, there exists an element $x\in X$ such that $HT^{x}=T^{x}H$. In this paper, we obtain some results about the $X$-$s$-permutable subgroups and use them to determine the structure of some finite groups. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2008.02.003 |
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