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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2011, Volume 8, Pages 39–47
(Mi semr298)
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Research papers
On $s$-semipermutable and weakly $s$-permutable subgroups
Ch. Li School of Mathematical Science, Xuzhou Normal University, Xuzhou, China
Abstract:
Let $H$ be a subgroup of a finite group $G$. $H$ is said to be $s$-semipermutable in $G$ if
$HG_{p}=G_{p}H$ for any Sylow $p$-subgroup $G_{p}$ of $G$ with $(p,|H|)=1$; $H$ is called weakly $s$-permutable in $G$ if there exists a subnormal subgroup $T$ of $G$ such that $G=HT$ and $H\cap T\leq
H_{sG}$, where $H_{sG}$ is the subgroup of $H$ generated by all those subgroups of $H$ which are $s$-permutable in $G$. We fix in every non-cyclic Sylow subgroup $P$ of $G$ a subgroup $D$ with
$1<|D|<|P|$ and study the structure of $G$ under the assumption that every subgroup $H$ of $P$ with
$|H|=|D|$ is either $s$-semipermutable or weakly $s$-permutable in $G$. Some recent results are generalized and unified.
Keywords:
$s$-semipermutable, weakly $s$-permutable, $p$-nilpotent, the generalized Fitting subgroup.
Received July 12, 2010, published January 24, 2011
Citation:
Ch. Li, “On $s$-semipermutable and weakly $s$-permutable subgroups”, Sib. Èlektron. Mat. Izv., 8 (2011), 39–47
Linking options:
https://www.mathnet.ru/eng/semr298 https://www.mathnet.ru/eng/semr/v8/p39
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Abstract page: | 337 | Full-text PDF : | 81 | References: | 73 |
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