Geodesic
On $X$-$s$-permutable subgroups of finite groups
Trudy Instituta matematiki, Tome 16 (2008) no. 1, pp. 100-105.

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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 $HT^x=T^xH$. In this paper we obtain some results on $X$-$s$-permutable subgroups and use them to determine the structure of some finite groups. 
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Lei Shi; Guo Wenbin; Yi Xiaolan. On $X$-$s$-permutable subgroups of finite groups. Trudy Instituta matematiki, Tome 16 (2008) no. 1, pp. 100-105. http://geodesic.mathdoc.fr/item/TIMB_2008_16_1_a17/

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