University of IsfahanInternational Journal of Group Theory2251-76505220160601Finite BCI-groups are solvable16726510.22108/ijgt.2016.7265ENMajidArezoomandIsfahan University of TechnologyBijanTaeriIsfahan University of TechnologyJournal Article20140411Let $S$ 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.https://ijgt.ui.ac.ir/article_7265_5d7f9ab8bf8b6c396bfac5b1e7a5f461.pdf