The minimum sum of element orders of finite groups

Document Type: Research Paper

Authors

1 Department of Mathematics, Shabestar branch, Islamic Azad University, Shabestar, Iran

2 Department of Mathematics, Shabestar Branch, Islamic Azad University, Shabestar, Iran

3 Department of Mathematics, Tabriz Branch, Islamic Azad University, Tabriz, Iran

Abstract

Let G be a finite group and $psi(G)=sum_{gin G}o(g)$, where $o(g)$ denote 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)

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