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Problemy Fiziki, Matematiki i Tekhniki (Problems of Physics, Mathematics and Technics), 2010, Issue 2(3), Pages 21–27 (Mi pfmt159)  

This article is cited in 10 scientific papers (total in 10 papers)

MATHEMATICS

On finite groups similar to supersoluble groups

A. F. Vasil'eva, T. I. Vasilyevab, V. N. Tyutyanova

a F. Skorina Gomel State University, Gomel
b Belarusian State University of Transport, Gomel
References:
Abstract: A subgroup $H$ of $G$ is called $\mathbf{P}$-subnormal in $G$ if either $H = G$ or there is a chain $H = H_0 \subset H_1 \subset \dots \subset H_{n-1} \subset H_n = G$ such that $|H_{i+1} : H_i |$ is a prime number for every $i = 0, 1, \dots , n-1$. For the set of $\pi$ primes the properties of $\mathrm w_\pi$-supersoluble groups $G$, i.e. groups for which for every $p \in \pi$ Sylow $p$-subgroup is $\mathbf{P}$-subnormal in $G$ are investigated. It is proved that the class of all $\mathrm w_\pi$-supersoluble groups is a normally hereditary formation, and the class of all soluble $\mathrm w_\pi$-supersoluble groups is a hereditary saturated formation. The properties of the groups, which are the product of $\mathbf{P}$-subnormal subgroups are obtained.
Keywords: finite group, $\mathbf{P}$-subnormal subgroup, $\mathrm w_\pi$-supersoluble group, formation, $\pi$-saturated formation.
Received: 06.05.2010
Document Type: Article
UDC: 512.542
Language: Russian
Citation: A. F. Vasil'ev, T. I. Vasilyeva, V. N. Tyutyanov, “On finite groups similar to supersoluble groups”, PFMT, 2010, no. 2(3), 21–27
Citation in format AMSBIB
\Bibitem{VasVasTyu10}
\by A.~F.~Vasil'ev, T.~I.~Vasilyeva, V.~N.~Tyutyanov
\paper On finite groups similar to supersoluble groups
\jour PFMT
\yr 2010
\issue 2(3)
\pages 21--27
\mathnet{http://mi.mathnet.ru/pfmt159}
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  • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Проблемы физики, математики и техники
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