University of Isfahan International Journal of Group Theory 2251-7650 10 2 2021 06 01 The minimum sum of element orders of finite groups 55 60 23858 10.22108/ijgt.2019.115910.1538 EN Maghsoud Jahani Department of Mathematics, Shabestar Branch, Islamic Azad University, Shabestar, Iran Yadollah Marefat Department of Mathematics, Shabestar branch, Islamic Azad University, Shabestar, Iran Hasan Refaghat Department of Mathematics, Tabriz Branch, Islamic Azad University, Tabriz, Iran Bahram Vakili Fasaghandisi Department of Mathematics, Shabestar branch, Islamic Azad University, Shabestar, Iran Journal Article 2019 03 07 ‎Let $ G $ be a finite group and \( \psi(G)=\sum_{g\in G}o(g) \)‎, ‎where $ o(g) $ denotes the order of $g\in G$‎. ‎We show that the Conjecture 4.6.5 posed in [Group Theory and Computation‎, ‎(2018) 59-90]‎, ‎is incorrect‎. ‎In fact‎, ‎we find a pair of finite groups $G$ and $S$ of the same order such that $ \psi(G)<\psi(S)$‎, ‎with $G$ solvable and $S$ simple‎. https://ijgt.ui.ac.ir/article_23858_0ac95daf1e2e870740851f216e4a425f.pdf