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Mat. Zametki, 2009, Volume 86, Issue 5, Pages 692–704 (Mi mz8513)  

This article is cited in 2 scientific papers (total in 2 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

DOI: https://doi.org/10.4213/mzm8513

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English version:
Mathematical Notes, 2009, 86:5, 655–664

Bibliographic databases:

UDC: 512.542
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

Citation in format AMSBIB
\Bibitem{Mia09}
\by Long Miao
\paper Finite Groups with Some Maximal Subgroups of Sylow Subgroups $\mathscr M$-Supplemented
\jour Mat. Zametki
\yr 2009
\vol 86
\issue 5
\pages 692--704
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\crossref{https://doi.org/10.4213/mzm8513}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2641343}
\zmath{https://zbmath.org/?q=an:1184.20016}
\transl
\jour Math. Notes
\yr 2009
\vol 86
\issue 5
\pages 655--664
\crossref{https://doi.org/10.1134/S000143460911008X}
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  • http://mi.mathnet.ru/eng/mz/v86/i5/p692

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Zhencai Shen, Shirong Li, Jinshan Zhang, “On SS-Quasinormal and S-Quasinormally Embedded Subgroups of Finite Groups”, Math. Notes, 95:2 (2014), 270–279  mathnet  crossref  crossref  mathscinet  isi  elib
    2. Guo J., Zhang J., Miao L., “On nearly $\mathscr M$-supplemented subgroups of finite groups”, Ukrainian Math. J., 66:1 (2014), 66–76  crossref  mathscinet  zmath  isi  scopus
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