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Problemy Fiziki, Matematiki i Tekhniki (Problems of Physics, Mathematics and Technics), 2015, Issue 1(22), Pages 82–87
(Mi pfmt362)
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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
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
Citation:
V. I. Murashka, “Soluble formations with the Shemetkov property”, PFMT, 2015, no. 1(22), 82–87
Linking options:
https://www.mathnet.ru/eng/pfmt362 https://www.mathnet.ru/eng/pfmt/y2015/i1/p82
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Abstract page: | 115 | Full-text PDF : | 42 | References: | 32 |
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