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Matematicheskie Zametki, 2009, Volume 86, Issue 5, Pages 692–704
DOI: https://doi.org/10.4213/mzm8513
(Mi mzm8513)
 

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
Full-text PDF (470 kB) Citations (3)
References:
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
English version:
Mathematical Notes, 2009, Volume 86, Issue 5, Pages 655–664
DOI: https://doi.org/10.1134/S000143460911008X
Bibliographic databases:
UDC: 512.542
Language: Russian
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
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\yr 2009
\vol 86
\issue 5
\pages 692--704
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\transl
\jour Math. Notes
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\pages 655--664
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  • https://doi.org/10.4213/mzm8513
  • https://www.mathnet.ru/eng/mzm/v86/i5/p692
  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математические заметки Mathematical Notes
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    References:78
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