Document Type: Original Manuscript

Author

Department of Mathematics, Tehran North Branch, Islamic Azad University, Tehran, IRAN.

Abstract

The prime graph of a finite group $G$ is denoted by
$ga(G)$. A nonabelian simple group $G$ is called quasirecognizable by prime
graph, if for every finite group $H$, where $ga(H)=ga(G)$, there
exists a nonabelian composition factor of $H$ which is isomorphic to
$G$. Until now, it is proved that some finite linear simple groups are
quasirecognizable by prime graph, for instance, the linear groups $L_n(2)$ and $L_n(3)$ are quasirecognizable by prime graph. In this paper, we consider the
quasirecognition by prime graph of the simple group $L_n(5)$.

Keywords