Journal of the
Korean Mathematical Society JKMS

In this paper we will prove that the simple groups $B_{p}(3)$ and $C_{p}(3)$, $p$ an odd prime number, are $2$-recognizable by the set of their order components. More precisely we will prove that if $G$ is a finite group and $% OC(G)$ denotes the set of order components of $G$, then $OC(G)=OC(B_{p}(3))$ if and only if $G\cong B_{p}(3)$ or $C_{p}(3).$

Keywords: prime graph, order component, linear group

MSC numbers: 20D06, 20D60