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Diskr. Mat., 2011, Volume 23, Issue 1, Pages 94–101 (Mi dm1133)  

This article is cited in 1 scientific paper (total in 1 paper)

The critical $\omega$-foliated $\tau$-closed formations of finite groups

M. A. Korpacheva, M. M. Sorokina


Abstract: Let $\mathfrak H$ be a class of finite groups, $\tau$ be a subgroup functor; an $\omega$-foliated $\tau$-closed formation of finite groups $\mathfrak F$ with direction $\delta$ is called the minimal $\omega$-foliated $\tau$-closed non-$\mathfrak H$-formation with direction $\delta$, or, in other words, $\mathfrak H_{\omega\tau\delta}$-critical formation if $\mathfrak F\not\subseteq\mathfrak H$, but all proper $\omega$-foliated $\tau$-closed subformations with direction $\delta$ in $\mathfrak F$ are contained in the class $\mathfrak H$. In this paper we investigate the structure of the minimal $\omega$-foliated $\tau$-closed non-$\mathfrak H$-formations with $bp$-direction $\delta$ satisfying the condition $\delta\le\delta_3$ in the case where $\tau$ is a regular $\delta$-radical subgroup functor.

DOI: https://doi.org/10.4213/dm1133

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English version:
Discrete Mathematics and Applications, 2011, 21:1, 69–77

Bibliographic databases:

UDC: 512.542
Received: 12.11.2008
Revised: 07.06.2009

Citation: M. A. Korpacheva, M. M. Sorokina, “The critical $\omega$-foliated $\tau$-closed formations of finite groups”, Diskr. Mat., 23:1 (2011), 94–101; Discrete Math. Appl., 21:1 (2011), 69–77

Citation in format AMSBIB
\Bibitem{KorSor11}
\by M.~A.~Korpacheva, M.~M.~Sorokina
\paper The critical $\omega$-foliated $\tau$-closed formations of finite groups
\jour Diskr. Mat.
\yr 2011
\vol 23
\issue 1
\pages 94--101
\mathnet{http://mi.mathnet.ru/dm1133}
\crossref{https://doi.org/10.4213/dm1133}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2830700}
\elib{http://elibrary.ru/item.asp?id=20730376}
\transl
\jour Discrete Math. Appl.
\yr 2011
\vol 21
\issue 1
\pages 69--77
\crossref{https://doi.org/10.1515/DMA.2011.005}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-79953328138}


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  • http://mi.mathnet.ru/eng/dm/v23/i1/p94

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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. V. A. Vedernikov, M. M. Sorokina, “On complements of coradicals of finite groups”, Sb. Math., 207:6 (2016), 792–815  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
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