Geodesic
Soluble groups with $\mathfrak{F}$-permutable subgroup
Kragujevac Journal of Mathematics, Tome 37 (2013) no. 2, p. 341 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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Let $G$ be a finite group and $\mathfrak{F}$ a class of finite groups. A subgroup $H$ of $G$ is said to be $\mathfrak{F}$-permutable in $G$ if there exists a subgroup $T$ of $G$ such that $HT$ is $s$-permutable in $G$ and $(H\cap T) H_{G}/H_{G}$ is contained in the $\mathfrak{F}$-hypercenter $Z_{\infty}^{\mathfrak{F}}(G/H_{G})$ of $G/H_{G}$. By using this new concept, we establish some new criteria for a group $G$ to be soluble.
Classification : 20D10 20D20
Keywords: $s$-permutable, $\mathfrak{F}$-permutable, Soluble groups 
@article{KJM_2013_37_2_a12,
     author = {Changwen Li and Yan Wang},
     title = {Soluble groups with $\mathfrak{F}$-permutable subgroup},
     journal = {Kragujevac Journal of Mathematics},
     pages = {341 },
     year = {2013},
     volume = {37},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KJM_2013_37_2_a12/}
}
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Changwen Li; Yan Wang. Soluble groups with $\mathfrak{F}$-permutable subgroup. Kragujevac Journal of Mathematics, Tome 37 (2013) no. 2, p. 341 . http://geodesic.mathdoc.fr/item/KJM_2013_37_2_a12/