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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.

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
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