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Problemy Fiziki, Matematiki i Tekhniki (Problems of Physics, Mathematics and Technics), 2015, Issue 1(22), Pages 82–87 (Mi pfmt362)  

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

MATHEMATICS

Soluble formations with the Shemetkov property

V. I. Murashka

Francisk Skorina Gomel State University
Full-text PDF (434 kB) Citations (1)
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Abstract: All saturated soluble formations whose all $s$-critical groups are soluble were described. With every local formation $\mathfrak{F}=LF(f)$, such that $f(p)=\mathfrak{S}_{\pi(f(p))}$ for all $p\in\pi(\mathfrak{F})$ and $f(p)=\varnothing$ otherwise, was associated directed graph $\Gamma(\mathfrak{F},f)$ without loops whose vertices are prime numbers from $\pi(\mathfrak{F})$ and $(p_i,p_j)$ is an edge of $\Gamma(\mathfrak{F},f)$ if and only if $p_j\in\pi(f(p_i))$. With the help of such kind’s graphs all hereditary soluble formations with the Shemetkov property were described.
Keywords: minimal simple group, $s$-critical group, hereditary local formation, formation with the Shemetkov property, graph associated with formation.
Received: 22.09.2014
Document Type: Article
UDC: 512.542
Language: English
Citation: V. I. Murashka, “Soluble formations with the Shemetkov property”, PFMT, 2015, no. 1(22), 82–87
Citation in format AMSBIB
\Bibitem{Mur15}
\by V.~I.~Murashka
\paper Soluble formations with the Shemetkov property
\jour PFMT
\yr 2015
\issue 1(22)
\pages 82--87
\mathnet{http://mi.mathnet.ru/pfmt362}
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  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Проблемы физики, математики и техники
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