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.
Arezoomand, M. and Taeri, B. (2016). Finite BCI-groups are solvable. International Journal of Group Theory, 5(2), 1-6. doi: 10.22108/ijgt.2016.7265
MLA
Arezoomand, M. , and Taeri, B. . "Finite BCI-groups are solvable", International Journal of Group Theory, 5, 2, 2016, 1-6. doi: 10.22108/ijgt.2016.7265
HARVARD
Arezoomand, M., Taeri, B. (2016). 'Finite BCI-groups are solvable', International Journal of Group Theory, 5(2), pp. 1-6. doi: 10.22108/ijgt.2016.7265
CHICAGO
M. Arezoomand and B. Taeri, "Finite BCI-groups are solvable," International Journal of Group Theory, 5 2 (2016): 1-6, doi: 10.22108/ijgt.2016.7265
VANCOUVER
Arezoomand, M., Taeri, B. Finite BCI-groups are solvable. International Journal of Group Theory, 2016; 5(2): 1-6. doi: 10.22108/ijgt.2016.7265
)
