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Sibirsk. Mat. Zh., 2016, Volume 57, Number 2, Pages 259–275 (Mi smj2742)  

This article is cited in 7 scientific papers (total in 7 papers)

Finite groups with generalized subnormal embedding of Sylow subgroups

A. F. Vasil'eva, T. I. Vasil'evab, A. S. Vegeraa

a Francisk Skaryna Gomel State University, Gomel, Belarus
b Belarusian State University of Transport, Gomel, Belarus

Abstract: Given a set $\pi$ of primes and a hereditary saturated formation $\mathfrak F$, we study the properties of the class of groups $G$ for which the identity subgroup and all Sylow $p$-subgroups are $\mathfrak F$-subnormal ($\mathrm K$-$\mathfrak F$-subnormal) in $G$ for each $p$ in $\pi$. We show that such a class is a hereditary saturated formation and find its maximal inner local screen. Some criteria are obtained for the membership of a group in a hereditary saturated formation in terms of its formation subnormal Sylow subgroups.

Keywords: finite group, Sylow subgroup, formation, hereditary saturated formation, $\mathfrak F$-subnormal subgroup, $\mathrm K$-$\mathfrak F$-subnormal subgroup, local screen.

DOI: https://doi.org/10.17377/smzh.2016.57.203

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English version:
Siberian Mathematical Journal, 2016, 57:2, 200–212

Bibliographic databases:

UDC: 512.542
Received: 24.04.2015

Citation: A. F. Vasil'ev, T. I. Vasil'eva, A. S. Vegera, “Finite groups with generalized subnormal embedding of Sylow subgroups”, Sibirsk. Mat. Zh., 57:2 (2016), 259–275; Siberian Math. J., 57:2 (2016), 200–212

Citation in format AMSBIB
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\by A.~F.~Vasil'ev, T.~I.~Vasil'eva, A.~S.~Vegera
\paper Finite groups with generalized subnormal embedding of Sylow subgroups
\jour Sibirsk. Mat. Zh.
\yr 2016
\vol 57
\issue 2
\pages 259--275
\mathnet{http://mi.mathnet.ru/smj2742}
\crossref{https://doi.org/10.17377/smzh.2016.57.203}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3510191}
\elib{http://elibrary.ru/item.asp?id=26237266}
\transl
\jour Siberian Math. J.
\yr 2016
\vol 57
\issue 2
\pages 200--212
\crossref{https://doi.org/10.1134/S0037446616020038}
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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, K. L. Parfenkov, “O konechnykh gruppakh s zadannoi troinoi faktorizatsiei”, PFMT, 2017, no. 3(32), 43–47  mathnet
    2. 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
    3. 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
    4. 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
    5. A. F. Vasilev, “Konechnye gruppy s silno $\mathrm{K}$-$\mathfrak{F}$-subnormalnymi silovskimi podgruppami”, PFMT, 2018, no. 4(37), 66–71  mathnet
    6. V. S. Monakhov, I. L. Sokhor, “On groups with formational subnormal Sylow subgroups”, J. Group Theory, 21:2 (2018), 273–287  crossref  mathscinet  zmath  isi  scopus
    7. A. F. Vasilev, A. G. Melchenko, “Konechnye gruppy s absolyutno formatsionno subnormalnymi silovskimi podgruppami”, PFMT, 2019, no. 4(41), 44–50  mathnet
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