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 _p (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.