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Partially $S$-embedded minimal subgroups of finite groups | ||
| International Journal of Group Theory | ||
| مقاله 2، دوره 2، شماره 4، اسفند 2013، صفحه 7-16 اصل مقاله (304.51 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2013.2751 | ||
| نویسندگان | ||
| Tao Zhao* 1؛ Qingliang Zhang2 | ||
| 1School of Science, Shandong University of Technology | ||
| 2School of Sciences, Nantong University | ||
| چکیده | ||
| Suppose that $H$ is a subgroup of $G$, then $H$ is said to be $s$-permutable in $G$, if $H$ permutes with every Sylow subgroup of $G$. If $HP=PH$ hold for every Sylow subgroup $P$ of $G$ with $(|P|, |H|)=1$), then $H$ is called an $s$-semipermutable subgroup of $G$. In this paper, we say that $H$ is partially $S$-embedded in $G$ if $G$ has a normal subgroup $T$ such that $HT$ is $s$-permutable in $G$ and $H\cap T\leq H_{\overline{s}G}$, where $H_{\overline{s}G}$ is generated by all $s$-semipermutable subgroups of $G$ contained in $H$. We investigate the influence of some partially $S$-embedded minimal subgroups on the nilpotency and supersolubility of a finite group $G$. A series of known results in the literature are unified and generalized. | ||
| کلیدواژهها | ||
| s-permutable subgroup؛ partially S-embedded subgroup؛ nilpotent group؛ Formation | ||
| مراجع | ||
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