Geodesic
On $S$-quasinormal and $c$-normal subgroups of a finite group
Czechoslovak Mathematical Journal, Tome 58 (2008) no. 4, pp. 1083-1095.

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Let $\cal F$ be a saturated formation containing the class of supersolvable groups and let $G$ be a finite group. The following theorems are presented: (1) $G\in \cal F$ if and only if there is a normal subgroup $H$ such that $G/H\in \cal F$ and every maximal subgroup of all Sylow subgroups of $H$ is either $c$-normal or $S$-quasinormally embedded in $G$. (2) $G\in \cal F$ if and only if there is a normal subgroup $H$ such that $G/H\in \cal F$ and every maximal subgroup of all Sylow subgroups of $F^*(H)$, the generalized Fitting subgroup of $H$, is either $c$-normal or $S$-quasinormally embedded in $G$. (3) $G\in \cal F$ if and only if there is a normal subgroup $H$ such that $G/H\in \cal F$ and every cyclic subgroup of $F^*(H)$ of prime order or order 4 is either $c$-normal or $S$-quasinormally embedded in $G$.
Classification : 20D10, 20D20, 20D40, 20E28
Keywords: $S$-quasinormally embedded subgroup; $c$-normal subgroup; $p$-nilpotent group; the generalized Fitting subgroup; saturated formation 
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     author = {Li, Shirong and Li, Yangming},
     title = {On $S$-quasinormal and $c$-normal subgroups of a finite group},
     journal = {Czechoslovak Mathematical Journal},
     pages = {1083--1095},
     publisher = {mathdoc},
     volume = {58},
     number = {4},
     year = {2008},
     mrnumber = {2471167},
     zbl = {1166.20013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2008__58_4_a14/}
}
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Li, Shirong; Li, Yangming. On $S$-quasinormal and $c$-normal subgroups of a finite group. Czechoslovak Mathematical Journal, Tome 58 (2008) no. 4, pp. 1083-1095. http://geodesic.mathdoc.fr/item/CMJ_2008__58_4_a14/