Geodesic
On Nearly $S$-Permutably Embedded Subgroups of Finite Groups
Matematičeskie zametki, Tome 91 (2012) no. 4, pp. 495-505

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Let $G$ be a finite group. A subgroup $H$ of $G$ is said to be $S$-permutable in $G$ if $HP=PH$ for all Sylow subgroups $P$ of $G$. A subgroup $A$ of a group $G$ is said to be $S$-permutably embedded in $G$ if for each Sylow subgroup of $A$ is also a Sylow of some $S$-permutable subgroup of $G$. In this paper, we analyze the following generalization of this concept. Let $H$ be a subgroup of a group $G$. Then we say that $H$ is nearly $S$-permutably embedded in $G$ if $G$ has a subgroup $T$ and an $S$-permutably embedded subgroup $C\le H$ such that $HT=G$ and $T\cap H\le C$. We study the structure of $G$ under the assumption that some subgroups of $G$ are nearly $S$-permutably embedded in $G$. Some known results are generalized.
Keywords: $S$-permutably embedded subgroup, saturated formation, maximal subgroup.
Mots-clés : solvable group, supersolvable group 
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     author = {Kh. Al-Sharo},
     title = {On {Nearly} $S${-Permutably} {Embedded} {Subgroups} of {Finite} {Groups}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {495--505},
     publisher = {mathdoc},
     volume = {91},
     number = {4},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2012_91_4_a1/}
}
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Kh. Al-Sharo. On Nearly $S$-Permutably Embedded Subgroups of Finite Groups. Matematičeskie zametki, Tome 91 (2012) no. 4, pp. 495-505. http://geodesic.mathdoc.fr/item/MZM_2012_91_4_a1/