Lucido, Maria Silvia; Moghaddamfar, Ali Reza Recognition of some linear groups over the binary field by the spectrum. (Russian, English) Zbl 1118.20026 Sib. Mat. Zh. 47, No. 1, 108-122 (2006); translation in Sib. Math. J. 47, No. 1, 86-96 (2006). Summary: We focus our attention on the linear groups \(L_n(2)\) and obtain some general properties of these groups. We show that the linear groups \(L_p(2)\), where 2 is a primitive root \(\text{mod\,}p\) and \(p\) is an odd prime, are recognizable by the 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 the spectrum. Cited in 1 Document MSC: 20D60 Arithmetic and combinatorial problems involving abstract finite groups 20D06 Simple groups: alternating groups and groups of Lie type 20G40 Linear algebraic groups over finite fields Keywords:Gruenberg-Kegel graphs; projective special linear groups; sets of element orders; recognizable groups; spectra of finite groups; recognition by spectrum PDFBibTeX XMLCite \textit{M. S. Lucido} and \textit{A. R. Moghaddamfar}, Sib. Mat. Zh. 47, No. 1, 108--122 (2006; Zbl 1118.20026); translation in Sib. Math. J. 47, No. 1, 86--96 (2006) Full Text: EuDML EMIS