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Mat. Zametki, 2006, Volume 79, Issue 1, Pages 87–94 (Mi mz2676)  

This article is cited in 2 scientific papers (total in 2 papers)

On Critical $\omega$-Fan Formations of Finite Groups

M. A. Korpacheva, M. M. Sorokina

I. G. Petrovsky Bryansk State University

Abstract: We consider finite groups only. Let $\omega$ be a nonempty subset of the set $P$ of all primes, and let $f\colon\omega\cup\{\omega'\}\to\{$formations of groups$\}$ and $\delta\colon P\to\{$nonempty Fitting formations of groups$\}$ be some functions. The formation consisting of all groups $G$ such that $G/O_\omega(G)\in f(\omega')$ and $G/G_{\delta(p)}\in f(p)$ for any $p\in\omega\cap\pi(G)$ is referred to as an $\omega$-fan formation with direction $\delta$. Let $\mathfrak H$ be some class of groups; an $\omega$-fan formation $\mathfrak F$ with direction $\delta$ is said to be an $\mathfrak H_{\omega\delta}$-critical formation if $\mathfrak F\nsubseteq\mathfrak H$ and any proper $\omega$-fan subformation with direction $\delta$ in $\mathfrak F$ is contained in the class $\mathfrak H$. In the paper, a description of the structure of the $\mathfrak H_{\omega\delta}$-critical formations is presented.

DOI: https://doi.org/10.4213/mzm2676

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English version:
Mathematical Notes, 2006, 79:1, 79–85

Bibliographic databases:

UDC: 512.542
Received: 18.05.2004
Revised: 10.02.2005

Citation: M. A. Korpacheva, M. M. Sorokina, “On Critical $\omega$-Fan Formations of Finite Groups”, Mat. Zametki, 79:1 (2006), 87–94; Math. Notes, 79:1 (2006), 79–85

Citation in format AMSBIB
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\paper On Critical $\omega$-Fan Formations of Finite Groups
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\pages 87--94
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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. M. A. Korpacheva, M. M. Sorokina, “The critical $\omega$-foliated $\tau$-closed formations of finite groups”, Discrete Math. Appl., 21:1 (2011), 69–77  mathnet  crossref  crossref  mathscinet  elib
    2. Korpacheva M.A., Sorokina M.M., “Kriticheskie $\Omega$-kanonicheskie formatsii multioperatornykh $T$-grupp”, Vestnik Bryanskogo gosudarstvennogo universiteta, 2011, no. 4, 19–22  elib
  • Математические заметки Mathematical Notes
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