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Problemy Fiziki, Matematiki i Tekhniki (Problems of Physics, Mathematics and Technics), 2010, Issue 2(3), Pages 21–27
(Mi pfmt159)
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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
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
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
Linking options:
https://www.mathnet.ru/eng/pfmt159 https://www.mathnet.ru/eng/pfmt/y2010/i2/p21
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