On X-Semipermutability of Some Subgroups of Finite Groups
Received:October 03, 2008  Revised:May 16, 2009
Key Word: finite groups   $X$-semipermutable subgroups   supersoluble groups   $p$-nilpotent groups.  
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant Nos.10771172; 10771180).
Author NameAffiliation
Jin Bao LI School of Mathematics and Statistics, Southwest University, Chongqing 400715, P. R. China 
Li Ping HAO School of Mathematical Sciences, Xuzhou Normal University, Jiangsu 221116, P. R. China 
Xiao Lan YI Department of Mathematics, Zhejiang University, Zhejiang 310007, P. R. China 
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      Let $A$ be a subgroup of a group $G$ and $X$ a nonempty subset of $G$. $A$ is said to be $X$-semipermutable in $G$ if $A$ has a supplement $T$ in $G$ such that $A$ is $X$-permutable with every subgroup of $T$. In this paper, we try to use the $X$-semipermutability of some subgroups to characterize the structure of finite groups.
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