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Finite BCI-groups are solvable | ||
| International Journal of Group Theory | ||
| مقاله 1، دوره 5، شماره 2، شهریور 2016، صفحه 1-6 اصل مقاله (184.55 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2016.7265 | ||
| نویسندگان | ||
| Majid Arezoomand؛ Bijan Taeri* | ||
| Isfahan University of Technology | ||
| چکیده | ||
| Let $S$ be a subset of a finite group $G$. The bi-Cayley graph $BCay(G,S)$ of $G$ with respect to $S$ is an undirected graph with vertex set $G\times\{1,2\}$ and edge set $\{\{(x,1),(sx,2)\}\mid x\in G, \ s\in S\}$. A bi-Cayley graph $BCay(G,S)$ is called a BCI-graph if for any bi-Cayley graph $BCay(G,T)$, whenever $BCay(G,S)\cong BCay(G,T)$ we have $T=gS^\alpha$ for some $g\in G$ and $\alpha\in Aut(G)$. A group $G$ is called a BCI-group if every bi-Cayley graph of $G$ is a BCI-graph. In this paper, we prove that every BCI-group is solvable. | ||
| کلیدواژهها | ||
| Bi-Cayley graph؛ graph isomorphism؛ solvable group | ||
| مراجع | ||
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