Geodesic
The sum of orders of elements in nonabelian groups of odd order
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 2, pp. 1698-1704.

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Denote by $\psi(G)$ the sum of the orders of the elements of a finite group $G$. We obtain an exact upper bound for $\psi(G)$ on the set of nonabelian groups of given odd order $n$ in terms of the minimal prime divisor of $n$. We also describe the finite groups on which this bound is achieved.
Keywords: orders of elements, solvable groups. 
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A. A. Buturlakin; A. F. Tereshchenko. The sum of orders of elements in nonabelian groups of odd order. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 2, pp. 1698-1704. http://geodesic.mathdoc.fr/item/SEMR_2021_18_2_a15/

[1] H. Amiri, S.M. Jafarian Amiri, I.M. Isaacs, “Sums of element orders in finite groups”, Commun. Algebra, 37:9 (2009), 2978–2980 | DOI | MR | Zbl

[2] M. Tărnăuceanu, “Detecting structural properties of finite groups by the sum of element orders”, Isr. J. Math., 238:2 (2020), 629–637 | DOI | MR | Zbl

[3] M. Herzog, P. Longobardi, M. Maj, “The second maximal groups with respect to the sum of element orders”, J. Pure Appl. Algebra, 225:3 (2021), 106531 | DOI | MR | Zbl

[4] M. Herzog, P. Longobardi, M. Maj, “An exact upper bound for sums of element orders in non-cyclic finite groups”, J. Pure Appl. Algebra, 222:7 (2018), 1628–1642 | DOI | MR | Zbl

[5] R. Shen, G. Chen, C. Wu, “On groups with the second largest value of the sum of element orders”, Commun. Algebra, 43:6 (2015), 2618–2631 | DOI | MR | Zbl

[6] Y. Berkovich, Groups of prime power order, Walter de Gruyter, Berlin, 2008 | MR | Zbl

[7] I.M. Isaacs, Finite group theory, American Mathematical Society, Providence, 2008 | MR | Zbl