[1]    Amiri, H., Jafarian Amir, S. M., Isaacs, I. M., Sums of element orders in finite groups, Comm. Algebra, 37(9) (2009), 2978-2980.
[2]    Amiri, H., Jafarian Amiri, S. M., Sum of element orders on finite groups of the same order, J. Algebra Appl., 10(02) (2011), 187–190.
[3]    Amiri, H., Jafarian Amiri, S. M., Sum of element orders of maximal subgroups of the symmetric group, Comm. Algebra, 40 (2012), 770-778.
[4]    Amiri, M., On the sum of element orders in finite abelian groups, J. Algebr. Comb., 63 (2026), Article No. 65.
[5]    Akhlaghi, Z., Khosravi, B., ZareZadeh, A., Characterizing some finite groups by the average order, Quaest. Math., 47 (2024), 2259–2270.
[6]    Baniasad Azada, M., Khosravia, B., Rashidi, H., On the sum of the inverses of the element orders in finite groups, Comm. Algebra, 51(2) (2023), 694–698.

[7]    Baniasad Azad, M., Khosravi, B., A criterion for p-nilpotency and p-closedness by the sum of element orders, Comm. Algebra, 48(12) (2020), 5391–5395.
[8]    Baniasad Azad, M., Khosravi, B., A criterion for solvability of a finite group by the sum of element orders, J. Algebra, 516 (2018), 115–124.
[9]    Bahri, A., Khosravi, B., Akhlaghi, Z., A result on the sum of element orders of a finite group., Arch. Math., 114 (2020), 3-12.
[10]    Baniasad Azad, M., Khosravi, B., Jafarpour, M., An answer to a conjecture on the sum of element orders, J. Algebra Appl. 21 (2022), 2250067.
111 2122920 Azad, M., Khosravi, ., On the sum of element orders of PSL(2 ,p) for some p, 1/47 J. Pure Appl. Math, 42 (2019), 18–24.
[12]    Buturlakin, A. A., Tereshchenko, A. F., The sum of orders of elements in nonabelian groups of odd order, Sib. Èlektron. Mat. Izv., 18 (2021), 1698–1704
[13]    Cameron, Peter J., Dey, Hiranya Kishore, On the order sequence of a group, Electron. J. Combin., Volume 32, Issue 2 (2025)
[14]    Das, A., Nath, R. K., Pournaki, M. R., A survey on the estimation of commutativity in finite groups, Southeast Asian Bull. Math., 37 (2013), 161–-180.
[15]    Domenico, E. D., Monetta, C., Noce, M., Upper bounds for the product of element orders of finite groups, J. Algebr. Comb., (2023) 57, 1033–1043.
[16]    Khosravi, B., Baniasad Azad, M., Recognition by the product element orders, Bull. Malays. Math. Sci. Soc., 43 (2020), 1183–1193.
[17]    Dey, H. K., The solvability of a finite group by the sum of powers of element orders, available at arXiv:2212.07748.
[18]    Dey, H. K., Mondal, A., An exact upper bound for the sum of powers of element orders in non-cyclic finite groups, J. Pure Appl. Algebra, 228 (6) (2024), 107580.
[19]    Garonzi, M., Patassini, M., Inequalities detecting structural properties of a finite group, Comm. Algebra, 45(2) (2017), 677–687.
[20]    Garonzi, M., Kappe, L.-C., Swartz, E. On integers that are covering numbers of groups, Experimental Mathematics, to appear.
[21]    Harrington, J., Jones, L., Lamarche, A., Characterizing finite groups using the sum of the orders of the elements, Int. J. Comb., 2014, 835125.
[22]    Harrington, J., Jones, L., Lamarche, A., Characterizing finite groups using the sum of the orders of the elements, Int. J. Comb., 2014, 835125.
[23]    Herzog, M., Longobardi, P., Maj, M., An exact upper bound for sums of element orders in non-cyclic finite groups, J. Pure Appl. Algebra, 222 (2018), 1628–1642.
[24]    Herzog, M., Longobardi, P., Maj, M., Two new criteria for solvability of finite groups in finite groups, J. Algebra, 511 (2018), 215–226
251    Herzog, M., Longobardi, P., Maj, M., Sums of element orders in groups of order 2m with m odd, Comm. Algebra, 47 (2019), 2035–2048
[26]    Herzog, M., Longobardi, P., Maj, M., On a criterion for solvability ofa finite groups. Comm. Algebra 49 (2021) 2234–2240.
[27]    Herzog, M., Longobardi, P., Maj, M., The second maximal groups with respect to the sum of element orders, J. Pure Appl. Algebra, 225:3 (2021).
[28]    Herzog, M., Longobardi, P., Maj, M., Properties of finite and periodic groups determined by their elements orders (a survey), in Group Theory and Computation, Indian Statistical Institute Series, 2018, 59–90.
[29]    Herzog, M., Longobardi, P., Maj, M., New criteria for solvability, nilpotency and other properties of finite groups in terms of the order elements or subgroups. Int. J. Group Theory 12(3) (2023) 35–44.

[30]    Herzog, M., Longobardi, P., Maj, M., Sums of element orders in groups of odd order, Internat. J. Algebra Comput. (2021).
[31]    Herzog, M., Longobardi, P., Maj, M., On groups with average element orders equal to the average element order of the alternating group of degree, Glasnik matematički, (2023),
[32]    Herzog, M., Longobardi, P., Maj, M., Another criterion for solvability of finite groups, J. Algebra 597 (2022), 1-23.
[33]    Herzog, M., Longobardi, P., Maj, M., Properties of finite and periodic groups determined by their element orders (a survey), in Indian Statistical Institute Series 59-90.
[34]    Herzog, M., Longobardi, P., Maj, M., Sums of element orders in groups of odd order, Internat. J. Algebra Comput., 31 (2021), 1049–1063.
[35]    Isaacs, I. M., Loukaki, M., Moret´o, A., The average degree of an irreducible character of a finite group.,Israel J. Math., (2013) 197, 55-67.
[36]    Isaacs, I. M., Navarro, G., Character correspondences and irreducible induction and restriction, J. Algebra, 140 (1991), no. 1, 131-140.
[37]    Isaacs, I. M., Navarro, G., Primes and conductors of characters, J. Algebra, 653 (2024), 42-53.
[38]    Jahani, M., Marefat, Y., Refaghat, H., Vakili Fasaghandisi, B., The minimum sum of element orders of finite groups, Inter. J. Group Theory, 10 (2021), 55-60.
397 Jafarian Amiri, S. M., Characterization of 45 and (0)51(2: 7) by sum of element orders, Int. J. Group Theory, 2 (2013), 35–39.
[40]    Jafarian Amiri, S. M., Second maximum sum of element orders on finite nilpotent groups, Comm. Algebra, 41 (2013), 2055–2059.
411 Jafarian Amiri, S. M., Maximum sum element orders of all proper subgroups of PGL(2, q), Bull.
Iranian Math. Soc., 39 (2013), 501-505.
[42]    Jafarian Amiri, S. M., Amiri, M., Second maximum sum of element orders on finite groups, Journal of Pure and Applied Algebra, 218 (2014), 531–539.
[43]    Jafarian Amiri, S. M. and Amiri, M., Sum of the products of the orders of two distinct elements in finite groups, Comm. Algebra, 42 (2014) 5319–5328.
[44]    Jafarian Amiri, S. M., Amiri, M., Characterization of p-groups by sum of the element orders, Publ. Math. Debrecen, 86 (2015), 31–37.
[45]    Jafarian Amiri, S. M., Amiri, M., Sum of the element orders in groups with the square-free orders, Bull. Malays. Math. Sci. Soc., 40 (2017), 1025–1034.
[46]    Jafarian Amiri, S. M., Amiri, M., Characterization of finite groups by a bijection with a divisible property on the element orders. Comm. Algebra, 45(8) (2017), 3396–3401.
[47]    Jaikin-Zapirain, A., On the number of conjugacy classes of finite nilpotent groups, Adv. Math., 227 (2011), 1129-1143.
[48]    Lazorec, M., On a divisibility property involving the sum of element orders, Bull. Malays. Math. Sci. Soc., 44 (2) (2021), 941-951.
[49]    Lazorec, M. S. On two problems about order sequences of finite groups. J. Algebr. Comb. 62, 29 (2025).
[50]    Marefat, Y., Iranmanesh, A., Tehranian, A., On the sum of element orders of finite simple groups, J. Algebra Appl., 12 (2013), 135–138.
[51]    Navarro, G., I. M. Isaacs, available at https://www.uv.es/gabriel/static/I.M.Isaa-cs.English.pdf.
[52]    Khukhro, E. I., Moret´o, A., Zarrin, M., The average element order and the number of conjugacy classes of finite groups, J. Algebra, 569 (1) (2021), 1-11.
[53]    Shen, R., Chen, G., Wu, C., On groups with the second largest value of the sum of element orders, Comm. Algebra, 43 (2015) 2618–2631.
[54]    Pakianathan, J., Shankar, K., Nilpotent numbers, Amer. Math. Monthly, 107(7) (2000), 631–634.

[55]    Passman, D., Memorial resolution for Marty Isaacs, available at https://math.wisc.edu/ documents/isaacs-memorial-by-passman.
[56]    Tarnauceanu, M., A generalization of a result on the sum of element orders of a finite group, Math. Slovaca, 71 (000000), 627-630.
[57]    Tarnauceanu, M. and Fodor, D. G., On the sum of element orders of finite abelian groups, An. Stiint. Univ. Al. I. Cuza Iasi. Mat., 60 (2014), 1–8.
[58]    Tarnauceanu, M., A criterion for nilpotency of a finite group by the sum of element orders, Comm.
Alg., 49 (4), 1571-1577.
[59]    Lazorec, M. S., Tarnauceanu, M. M., On the average order of a finite group, J. Pure Appl. Algebra,
227 (4) (2023), 107276.
[60]    Lazorec, M., Tarnauceanu, M., A density result on the sum of element orders of a finite group, Arch.
Math., 114 (6) (2020), 601-607.
[61]    Tarnauceanu, M., Detecting structural properties of finite groups by the sum of element orders, Israel J. Math., 2020.
[62]    Tarnauceanu, M., Another criterion for supersolvability of finite groups, J. Algebra, 604 (2022), 682-693.
[63]    Vieira Marques, A., Sobre a soma das ordens de elementos de um grupo finito (2020), available at http://repositorio2.unb.br/jspui/handle/10482/39669.
[64]    Tarnauceanu, M., A note on the product of element orders of finite Abelian groups, Bull. Malays.
Math. Sci. Soc., 36(4) (2013), 1123–1126.