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Characterizations of Chevalley groups using order of the finite groups. (English) Zbl 1448.20013

Summary: In this paper, we prove \(\psi (A_1(4)) < \psi(G), \forall\) groups which are not simple with order sixty, \(A_1(4)\) is Chevalley group (Linear group) of order 60. Also we prove that \(\psi (A_2(2)) < \psi(G)\) using higher order non-simple groups of order 168.

MSC:

20D05 Finite simple groups and their classification
20-08 Computational methods for problems pertaining to group theory
20D60 Arithmetic and combinatorial problems involving abstract finite groups
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References:

[1] Amiri, H., Jafarian Amiri, S. M., & Isaacs, I. M. (2009). Sums of element orders in finite groups.Communications in Algebra, 37(9), 2978-2980. · Zbl 1183.20022
[2] Amiri, H., & Jafarian Amiri, S. M. (2011). Sum of element orders on finite groups of the same order.Journal of Algebra and its Applications, 10(02), 187-190. 187-190. · Zbl 1217.20015
[3] Mabuchi, T. (1990). Compactification of the Moduli Space of Einstein-Khler Orbifolds. In Recent Topics in Differential and Analytic Geometry(pp. 359-384). Academic Press. · Zbl 0747.32020
[4] Isaacs, I. M. (2008).Finite group theory(Vol. 92). American Mathematical Soc. · Zbl 1169.20001
[5] Amiri, H., & Jafarian Amiri, S. M. (2012). Sum of element orders of maximal subgroups of the symmetric group.Communications in Algebra, 40(2), 770-778. · Zbl 1239.20026
[6] Tufail, M., & Qazi, R. (2019). A closer look at multiplication table of finite rings.Open Journal of Mathematical Sciences., 3(1), 285 288.
[7] Chelgham, M., & Kerada, M. (2018).On Torsion and finite extension ofF Candτ NK groups in certain classes of finitely generated groups.Open Journal of Mathematical Sciences., 2(1), 351 360.
[8] Abdullateef, L.
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