Mazurov, V. D. Recognition of the finite simple groups \(S_4(q)\) by their element orders. (Russian, English) Zbl 1067.20016 Algebra Logika 41, No. 2, 166-198 (2002); translation in Algebra Logic 41, No. 2, 93-110 (2002). It is proved that among the simple groups \(S_4(q)\) in the class of finite groups, only the groups \(S_4(3^n)\), where \(n\) is an odd number greater than one, are recognizable by the set of their element orders. It is also shown that the simple groups \(U_3(9)\), \(^3D_4(2)\), \(G_2(4)\), \(S_6(3)\), \(F_4(2)\), and \(^2E_6(2)\) are recognizable, but \(L_3(3)\) is not. Reviewer: K. N. Ponomarev (Novosibirsk) Cited in 1 ReviewCited in 25 Documents MSC: 20D06 Simple groups: alternating groups and groups of Lie type 20D60 Arithmetic and combinatorial problems involving abstract finite groups 20D20 Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure Keywords:finite simple groups; recognizability; sets of element orders PDFBibTeX XMLCite \textit{V. D. Mazurov}, Algebra Logika 41, No. 2, 166--198 (2002; Zbl 1067.20016); translation in Algebra Logic 41, No. 2, 93--110 (2002)