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JOURNALS // Problemy Fiziki, Matematiki i Tekhniki (Problems of Physics, Mathematics and Technics) // Archive

PFMT, 2015 Issue 1(22), Pages 82–87 (Mi pfmt362)

This article is cited 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.

UDC: 512.542

Received: 22.09.2014

Language: English



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