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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     author = {A. A. Buturlakin and A. F. Tereshchenko},
     title = {The sum of orders of elements in nonabelian groups of odd order},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1698--1704},
     publisher = {mathdoc},
     volume = {18},
     number = {2},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2021_18_2_a15/}
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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/