@article { author = {Yi, X. and Yang, X.}, title = {Finite groups with $X$-quasipermutable subgroups of prime power order}, journal = {Bulletin of the Iranian Mathematical Society}, volume = {42}, number = {2}, pages = {407-416}, year = {2016}, publisher = {Iranian Mathematical Society (IMS)}, issn = {1017-060X}, eissn = {1735-8515}, doi = {}, abstract = {Let $H$, $L$ and $X$ be subgroups of a finite group $G$. Then $H$ is said to be $X$-permutable with $L$ if for some$xin X$ we have $AL^{x}=L^{x}A$. We say that $H$ is  emph{$X$-quasipermutable } (emph{$X_{S}$-quasipermutable}, respectively) in $G$ provided $G$ has a subgroup $B$ such that $G=N_{G}(H)B$ and $H$ $X$-permutes  with $B$ and with all subgroups (with all Sylow subgroups, respectively) $V$ of $B$ such that $(|H|, |V|)=1$. In this paper, we analyze the influence of $X$-quasipermutable and $X_{S}$-quasipermutable subgroups on the structure of $G$. Some known results are generalized.}, keywords = {$X$-quasipermutable subgroup,Sylow subgroup,$p$-soluble group,$p$-supersoluble group,$p$-nilpotent group}, url = {http://bims.iranjournals.ir/article_767.html}, eprint = {http://bims.iranjournals.ir/article_767_7c8f57226de334e589c125523eea2281.pdf} }