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This article is cited in 3 scientific papers (total in 3 papers)
Finite Groups with Some Maximal Subgroups of Sylow Subgroups $\mathscr M$-Supplemented
Long Miao Yangzhou University
Abstract:
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 $TB<G$ 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, formation, finite group, supersolvable group, Hall subgroup, Fitting subgroup, $p$-nilpotent group.
Received: 29.03.2008 Revised: 29.06.2008
Citation:
Long Miao, “Finite Groups with Some Maximal Subgroups of Sylow Subgroups $\mathscr M$-Supplemented”, Mat. Zametki, 86:5 (2009), 692–704; Math. Notes, 86:5 (2009), 655–664
Linking options:
https://www.mathnet.ru/eng/mzm8513https://doi.org/10.4213/mzm8513 https://www.mathnet.ru/eng/mzm/v86/i5/p692
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Abstract page: | 501 | Full-text PDF : | 164 | References: | 77 | First page: | 8 |
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