Characterization of some projective special linear groups in dimension four by their orders and degree patterns

‎Let $G$ be a finite group‎. ‎The degree pattern of $G$ denoted by‎ ‎$D(G)$ is defined as follows‎: ‎If $\pi(G)=\{p_{1},p_{2},...,p_{k}\}$ such that‎ ‎$p_{1} < p_{2} < ... < p_{k}$‎, ‎then $D(G):=(deg(p_{1}),deg(p_{2}),...,deg(p_{k}))$‎, ‎where $deg(p_{i})$‎ ‎for $1\leq i\leq k$‎, ‎are the degree of vertices $p_{i}$ in the‎ ‎prime graph of $G$‎. ‎In this article < , > we consider a finite group $G$‎ ‎under assumptions $|G|=|L_{4}(2^{n})|$ and $D(G)=D(L_{4}(2^{n}))$‎, ‎where $n\in\{5‎, ‎6‎, ‎7\}$ and we prove that $G\cong L_{4}(2^{n})$.