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PFMT, 2010, Issue 2(3), Pages 21–27 (Mi pfmt159)  

This article is cited in 10 scientific papers (total in 10 papers)

MATHEMATICS

On finite groups similar to supersoluble groups

A. F. Vasil'eva, T. I. Vasilyevab, V. N. Tyutyanova

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

Abstract: A subgroup $H$ of $G$ is called $\mathbf{P}$-subnormal in $G$ if either $H = G$ or there is a chain $H = H_0 \subset H_1 \subset …\subset H_{n-1} \subset H_n = G$ such that $|H_{i+1} : H_i |$ is a prime number for every $i = 0, 1, …, n-1$. For the set of $\pi$ primes the properties of $\mathrm w_\pi$-supersoluble groups $G$, i.e. groups for which for every $p \in \pi$ Sylow $p$-subgroup is $\mathbf{P}$-subnormal in $G$ are investigated. It is proved that the class of all $\mathrm w_\pi$-supersoluble groups is a normally hereditary formation, and the class of all soluble $\mathrm w_\pi$-supersoluble groups is a hereditary saturated formation. The properties of the groups, which are the product of $\mathbf{P}$-subnormal subgroups are obtained.

Keywords: finite group, $\mathbf{P}$-subnormal subgroup, $\mathrm w_\pi$-supersoluble group, formation, $\pi$-saturated formation

Full text: PDF file (436 kB)
References: PDF file   HTML file
UDC: 512.542
Received: 06.05.2010

Citation: A. F. Vasil'ev, T. I. Vasilyeva, V. N. Tyutyanov, “On finite groups similar to supersoluble groups”, PFMT, 2010, no. 2(3), 21–27

Citation in format AMSBIB
\Bibitem{VasVasTyu10}
\by A.~F.~Vasil'ev, T.~I.~Vasilyeva, V.~N.~Tyutyanov
\paper On finite groups similar to supersoluble groups
\jour PFMT
\yr 2010
\issue 2(3)
\pages 21--27
\mathnet{http://mi.mathnet.ru/pfmt159}


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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. F. Vasilev, T. I. Vasileva, “O konechnykh gruppakh s obobschenno subnormalnymi silovskimi podgruppami”, PFMT, 2011, no. 4(9), 86–91  mathnet
    2. V. N. Knyagina, “Konechnye gruppy s $\mathbb{P}$-subnormalnymi biprimarnymi podgruppami”, Tr. In-ta matem., 21:1 (2013), 63–68  mathnet
    3. A. F. Vasil'ev, T. I. Vasilyeva, V. N. Tyutyanov, “On $\mathrm K$-$\mathbb P$-Subnormal Subgroups of Finite Groups”, Math. Notes, 95:4 (2014), 471–480  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. V. N. Tyutyanov, T. V. Tikhonenko, “O konechnykh gruppakh s zadannoi sistemoi silovskikh podgrupp”, PFMT, 2014, no. 3(20), 85–87  mathnet
    5. V. N. Tyutyanov, P. V. Bychkov, “O konechnykh gruppakh s minimalnymi $\mathbb{P}$-subnormalnymi podgruppami”, PFMT, 2014, no. 4(21), 97–99  mathnet
    6. 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
    7. V. S. Monakhov, “Finite groups with abnormal and $\mathfrak U$-subnormal subgroups”, Siberian Math. J., 57:2 (2016), 352–363  mathnet  crossref  crossref  mathscinet  isi  elib
    8. E. N. Myslovets, A. F. Vasilev, “Konechnye obobschenno $c$-sverkhrazreshimye gruppy i ikh vzaimno perestanovochnye proizvedeniya”, PFMT, 2016, no. 2(27), 45–53  mathnet
    9. V. A. Kovaleva, “Konechnye gruppy s zadannymi obobschenno maksimalnymi podgruppami (obzor). II. Ot maksimalnykh tsepei k maksimalnym param”, PFMT, 2017, no. 2(31), 55–65  mathnet
    10. V. N. Tyutyanov, A. A. Trofimuk, “Tsepi v konechnykh gruppakh”, PFMT, 2019, no. 4(41), 70–73  mathnet
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