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Sibirskii Matematicheskii Zhurnal, 2008, Volume 49, Number 2, Pages 367–373
(Mi smj1846)
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This article is cited in 2 scientific papers (total in 2 papers)
Finite groups with $\mathscr F$-subnormal conditions
Sh. Lia, N. Dub a Department of Mathematics, Guangxi University
b College of Mathematics, Xiamen University
Abstract:
Let $\mathscr F$ be a subgroup-closed saturated formation. A finite group $G$ is called an $\mathscr F_{pc}$-group provided that each subgroup $X$ of $G$ is $\mathscr F$-subabnormal in the $\mathscr F$-subnormal closure of $X$ in $G$. Let $\mathscr F_{pc}$ be the class of all $\mathscr F_{pc}$-groups. We study some properties of $\mathscr F_{pc}$-groups and describe the structure of $\mathscr F_{pc}$-groups when $\mathscr F$ is the class of all soluble $\pi$-closed groups, where $\pi$ is a given nonempty set of prime numbers.
Keywords:
$\mathscr F$-subnormal subgroup, $\mathscr F$-projector, $\mathscr F$-covering subgroup, $\mathscr F_{pc}$-group.
Received: 21.06.2006 Revised: 20.10.2006
Citation:
Sh. Li, N. Du, “Finite groups with $\mathscr F$-subnormal conditions”, Sibirsk. Mat. Zh., 49:2 (2008), 367–373; Siberian Math. J., 49:2 (2008), 295–299
Linking options:
https://www.mathnet.ru/eng/smj1846 https://www.mathnet.ru/eng/smj/v49/i2/p367
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Abstract page: | 265 | Full-text PDF : | 72 | References: | 37 |
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