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On weakly $SS$-quasinormal and hypercyclically embedded properties of finite groups | ||
| International Journal of Group Theory | ||
| مقاله 3، دوره 3، شماره 4، اسفند 2014، صفحه 17-25 اصل مقاله (297.08 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2014.4950 | ||
| نویسنده | ||
| Tao Zhao* | ||
| School of Science, Shandong University of Technology | ||
| چکیده | ||
| A subgroup $H$ is said to be $s$-permutable in a group $G$, if $HP=PH$ holds for every Sylow subgroup $P$ of $G$. If there exists a subgroup $B$ of $G$ such that $HB=G$ and $H$ permutes with every Sylow subgroup of $B$, then $H$ is said to be $SS$-quasinormal in $G$. In this paper, we say that $H$ is a weakly $SS$-quasinormal subgroup of $G$, if there is a normal subgroup $T$ of $G$ such that $HT$ is $s$-permutable and $H\cap T$ is $SS$-quasinormal in $G$. By assuming that some subgroups of $G$ with prime power order have the weakly $SS$-quasinormal properties, we get some new characterizations about the hypercyclically embedded subgroups of $G$. A series of known results in the literature are unified and generalized. | ||
| کلیدواژهها | ||
| $s$-permutable؛ weakly $SS$-quasinormal؛ $p$-nilpotent؛ hypercyclically embedded | ||
| مراجع | ||
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