A characterization of some projective special linear groups

Abstract

In this paper, we show that projective special linear groups $S:=L_3(q)$ with $q$ less than $100$ are uniquely determined by their orders and degree patterns of their prime graphs. Indeed, we prove that if $G$ is a finite group whose order and degree pattern of its prime graph is the same as the order and the degree pattern of $S$, then $G$ is isomorphic to $S$.