University of Isfahan International Journal of Group Theory 2251-7650 5 2 2016 06 01 Finite BCI-groups are solvable 1 6 7265 10.22108/ijgt.2016.7265 EN Majid Arezoomand Isfahan University of Technology Bijan Taeri Isfahan University of Technology Journal Article 2014 04 11 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. https://ijgt.ui.ac.ir/article_7265_5d7f9ab8bf8b6c396bfac5b1e7a5f461.pdf