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PFMT, 2011, Issue 4(9), Pages 86–91 (Mi pfmt144)  

This article is cited in 8 scientific papers (total in 8 papers)

MATHEMATICS

On finite groups with generally subnormal sylow subgroups

A. F. Vasil'eva, T. I. Vasilyevab

a F. Skorina Gomel State University, Gomel
b Belarusian State University of Transport, Gomel

Abstract: Let $\mathfrak{F}$ be a non-empty formation. A subgroup $H$ of group $G$ is called $\mathfrak{F}$-subnormal in $G$ if either $H = G$ or there is a chain of subgroups $H = H_0 \subset H_1 \subset …\subset H_n = G$ such that $H_i^{\mathfrak{F}} \subseteq H_{i-1}$ for every $i = 1, …, n$. In the work the class of groups $w\mathfrak{F} = (G \mid\pi(G) \subseteq \pi(\mathfrak{F})$ and every Sylow subgroup of $G$ is $\mathfrak{F}$-subnormal in $G)$ are studied. Properties of the class $w\mathfrak{F}$ are obtained. In particular, for hereditary saturated formation $\mathfrak{F}$ it is proved that the class $w\mathfrak{F}$ is a hereditary saturated formation. Necessary and sufficient conditions are found, at which $w\mathfrak{F} = F$.

Keywords: finite group, Sylow subgroup, $\mathfrak{F}$-subnormal subgroup, hereditary formation, saturated formation

Full text: PDF file (381 kB)
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UDC: 512.542
Received: 09.09.2011

Citation: A. F. Vasil'ev, T. I. Vasilyeva, “On finite groups with generally subnormal sylow subgroups”, PFMT, 2011, no. 4(9), 86–91

Citation in format AMSBIB
\Bibitem{VasVas11}
\by A.~F.~Vasil'ev, T.~I.~Vasilyeva
\paper On finite groups with generally subnormal sylow subgroups
\jour PFMT
\yr 2011
\issue 4(9)
\pages 86--91
\mathnet{http://mi.mathnet.ru/pfmt144}


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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. A. S. Vegera, “O lokalnykh svoistvakh formatsii vsekh grupp s $\mathrm{K}$-$\mathfrak{F}$-subnormalnymi silovskimi podgruppami”, PFMT, 2014, no. 3(20), 53–57  mathnet
    2. V. I. Murashka, “Classes of finite groups with generalized subnormal cyclic primary subgroups”, Siberian Math. J., 55:6 (2014), 1105–1115  mathnet  crossref  mathscinet  isi
    3. A. F. Vasil'ev, T. I. Vasil'eva, A. S. Vegera, “Finite groups with generalized subnormal embedding of Sylow subgroups”, Siberian Math. J., 57:2 (2016), 200–212  mathnet  crossref  crossref  mathscinet  isi  elib
    4. A. F. Vasilev, T. I. Vasileva, K. L. Parfenkov, “O konechnykh gruppakh s zadannoi troinoi faktorizatsiei”, PFMT, 2017, no. 3(32), 43–47  mathnet
    5. V. S. Monakhov, I. L. Sokhor, “Finite groups with formation subnormal primary subgroups”, Siberian Math. J., 58:4 (2017), 663–671  mathnet  crossref  crossref  isi  elib  elib
    6. T. I. Vasileva, S. V. Balychev, “O vliyanii $k$-primarnykh khollovykh podgrupp na stroenie konechnykh razreshimykh grupp”, PFMT, 2018, no. 1(34), 55–60  mathnet
    7. A. F. Vasil'ev, T. I. Vasil'eva, K. L. Parfenkov, “Finite groups with three given subgroups”, Siberian Math. J., 59:1 (2018), 50–58  mathnet  crossref  crossref  isi  elib
    8. A. F. Vasilev, “Konechnye gruppy s silno $\mathrm{K}$-$\mathfrak{F}$-subnormalnymi silovskimi podgruppami”, PFMT, 2018, no. 4(37), 66–71  mathnet
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