Geodesic
Finite Groups with Some Maximal Subgroups of Sylow Subgroups $\mathscr M$-Supplemented
Matematičeskie zametki, Tome 86 (2009) no. 5, pp. 692-704

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A subgroup $H$ of a group $G$ is said to be $\mathscr M$‑supplemented in $G$ if there exists a subgroup $B$ of $G$ such that $G=HB$ and $TB$ for every maximal subgroup $T$ of $H$. In this paper, we obtain the following statement: Let $\mathscr F$ be a saturated formation containing all supersolvable groups and $H$ be a normal subgroup of $G$ such that $G/H\in\mathscr F$. Suppose that every maximal subgroup of a noncyclic Sylow subgroup of $F^{*}(H)$, having no supersolvable supplement in $G$, is $\mathscr M$-supplemented in $G$. Then $G\in\mathscr F$.
Keywords: Sylow subgroup, $\mathscr M$-supplemented subgroup, finite group, Hall subgroup, Fitting subgroup, $p$-nilpotent group.
Mots-clés : formation, supersolvable group 
@article{MZM_2009_86_5_a6,
     author = {Long Miao},
     title = {Finite {Groups} with {Some} {Maximal} {Subgroups} of {Sylow} {Subgroups} $\mathscr M${-Supplemented}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {692--704},
     publisher = {mathdoc},
     volume = {86},
     number = {5},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2009_86_5_a6/}
}
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Long Miao. Finite Groups with Some Maximal Subgroups of Sylow Subgroups $\mathscr M$-Supplemented. Matematičeskie zametki, Tome 86 (2009) no. 5, pp. 692-704. http://geodesic.mathdoc.fr/item/MZM_2009_86_5_a6/