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Some results on the join graph of finite groups | ||
| International Journal of Group Theory | ||
| دوره 10، شماره 4، اسفند 2021، صفحه 175-186 اصل مقاله (224.84 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2020.123287.1625 | ||
| نویسندگان | ||
| Zahara Bahrami؛ Bijan Taeri* | ||
| Department of Mathematical Sciences, Isfahan University of Technology, P.O.Box 84156-83111, Isfahan, Iran | ||
| چکیده | ||
| Let $G$ be a finite group which is not cyclic of prime power order. The join graph $\Delta(G)$ of $G$ is a graph whose vertex set is the set of all proper subgroups of $G$, which are not contained in the Frattini subgroup $G$ and two distinct vertices $H$ and $K$ are adjacent if and only if $G=\langle H, K\rangle$. Among other results, we show that if $G$ is a finite cyclic group and $H$ is a finite group such that $\Delta(G)\cong\Delta(H)$, then $H$ is cyclic. Also we prove that $\Delta(G)\cong\Delta(A_5)$ if and only if $G\cong A_5$. | ||
| کلیدواژه‌ها | ||
| Finite group؛ join graph؛ cyclic group؛ alternating group | ||
| مراجع | ||
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