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arXiv · 2608.10036

On a divisibility condition related to the sum of element orders of a finite group

Marius Tărnăuceanu
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Abstract

Given a finite group $G$, we denote by $\psi(G)$ the sum of element orders of $G$. In this note, we determine finite groups $G$ such that $|H|-|K|$ divides $\psi(H)-\psi(K)$ for all subgroups $K\leq H\leq G$. Two weaker conditions are also proposed.

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Marius Tărnăuceanu. 2026-08-10. On a divisibility condition related to the sum of element orders of a finite group. https://arxiv.org/abs/2608.10036

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