[1] H. Amiri, S. M. Jafarian Amiri and I. M. Isaacs, Sums of element orders in finite groups, Comm. Algebra, 37 (2009) 2978–2980.
[2] A. Bahri, B. Khosravi and Z. Akhlaghi, A result on the sum of element orders of a finite groups, Arch. Math. (Basel), 114 (2020) 3–12.
[3] M. Baniasad Azad and B. Khosravi, A criterion for solvability of a finite group by the sum of element orders, J. Algebra, 516 (2018) 115–124.
[4] M. Baniasad Azad, B. Khosravi and M. Jafarpour, An answer to a conjecture on the sum of element orders, J. Algebra Appl., (2021), to appear.
[5] R. Bastos and C. Monetta, Coprime commutators in finite groups, Comm. Algebra, 47 (2019) 4137–4147.
[6] R. Bastos and P. Shumyatsky, A sufficient condition for nilpotency of the commutator subgroup, Sib. Math. J., 57 (2016) 762–763.
[7] R. Bastos, C. Monetta and P. Shumyatsky, A criterion for metanilpotency of a finite group, J. Group Theory, 21 (2018) 713–718.
[8] B. Baumslag and J. Wiegold, A sufficient condition for nilpotency in a finite group, arXiv:1411.2877v1.
[9] T. De Medts and M. Tărnăuceanu, Finite groups determined by an inequality of the orders of their subgroups, Bull. Belg. Math. Soc. Simon Stevin, 15 (2008) 699–704.
[10] E. Fisman and Z. Arad, A proof of Szep’s conjecture, J. Algebra, 108 (1987) 340–354.
[11] M. Garonzi and I. Lima, On the Number of Cyclic Subgroups of a Finite Group, Bull. Braz. Math. Soc. New Series, 49 (2018) 515–530.
[12] M. Garonzi and M. Patassini, Inequalities detecting structural properties of a finite group, Comm. Algebra, 45 (2016) 677–687.
[13] M. Herzog, P. Longobardi and M. Maj, Two new criteria for solvability of finite groups, J. Algebra, 511 (2018) 215–226.
[14] M. Herzog, P. Longobardi and M. Maj, An exact upper bound for sums of elements order in non-cyclic finite groups, J. Pure Appl. Algebra, 222 (2018) 1628–1642.
[15] M. Herzog, P. Longobardi and M. Maj, On a criterion for solvability of a finite groups, Comm. Algebra, 49 (2021) 2234–2240.
[16] M. Herzog, P. Longobardi and M. Maj, Another criterion for solvability of finite groups, J. Algebra, (2022), to appear, arXiv:2112.04220.
[17] M. Herzog, P. Longobardi and M. Maj, Sums of element orders in groups of order 2m with m odd, Comm. Algebra, 47 (2019) 2035–2048.
[18] A. Jaikin-Zapirain, On the number of conjugacy classes of finite nilpotent groups, Advances in Math., 227 (2011) 1129–1143.
[19] E.I. Khukhro, A. Moretó and M. Zarrin, The average element order and the number of conjugacy classes of finite groups, J. Algebra, 569 (2021) 1–11.
[20] M. Lazorec and M. Tărnăuceanu, A density result on the sum of element orders of a finite group, Arch. Math., 114 (2020) 601–607.
[21] C. Monetta and A. Tortora, A nilpotency criterion for some verbal subgroups, Bull. Aust. Math. Soc., 100 (2019) 281–289.
[22] W. R. Scott, Group Theory, Prentice Hall, Inc., Englewood Cliffs, New Jersey, 1964.
[23] M. Tărnăuceanu, On the solvability of a finite group by the sum of subgroup orders, Bull. Korean Math. Soc., 57 (2020) 1475–1479.
[24] M. Tărnăuceanu, Finite groups determined by an inequality of the orders of their subgroups II, Comm. Algebra, 45 (2017) 4865–4868.
[25] M. Tărnăuceanu, A criterion for nilpotency of a finite group by the sum of element orders, Comm. Algebra, 49 (2021) 1571–1577.
[26] M. Tărnăuceanu, A nilpotency criterion for finite groups, Acta Math. Hungar., 155 (2018) 499–501.
[27] M. Tărnăuceanu, Detecting structural properties of finite groups by the sum of element orders, Israel. J. Math., 238 (2020) 629–637.
[28] M. Tărnăuceanu, A result on the number of cyclic subgroups of a finite group, Proc. Japan Acad., Ser. A, 96 (2020) 93–94.