Geodesic
On $s$-semipermutable and weakly $s$-permutable subgroups
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 8 (2011), pp. 39-47.

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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: weakly $s$-permutable, $p$-nilpotent, the generalized Fitting subgroup.
Mots-clés : $s$-semipermutable 
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     title = {On $s$-semipermutable and weakly $s$-permutable subgroups},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
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Ch. Li. On $s$-semipermutable and weakly $s$-permutable subgroups. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 8 (2011), pp. 39-47. http://geodesic.mathdoc.fr/item/SEMR_2011_8_a3/

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