| On X-s-Permutable Subgroups of a Finite Group |
| Received:August 28, 2008 Revised:May 18, 2009 |
| Key Words:
finite group $X$-$s$-permutable subgroup the generalized Fitting subgroup formation.
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant No.10871210) and the Natural Science Foundation of Guangdong Province (Grant No.06023728). |
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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 there exists an element $x\in X$ such that $HP^x = P^xH$ for every Sylow subgroup $P$ of $G$. In this paper, some new results are given under the assumption that some suited subgroups of $G$ are $X$-$s$-permutable in $G$. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2010.05.015 |
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