Recognition by spectrum of some linear groups over the binary field

We focus our attention on the linear groups $L_n(2)$ and obtain some general properties of these groups. We will show then that the linear groups $L_n(2)$, where 2 is a primitive root mod $p$ ($p$ odd prime), are recognizable by spectrum. For example, the linear groups $L_3(2)$, $L_5(2)$, $L_{11}(2)$, $L_{13}(2)$, $L_{19}(2)$, $L_{29}(2)$, $L_{37}(2)$, $L_{53}(2)$, etc. are recognizable by spectrum.