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arXiv · 2608.10035

Two new functions related to the sum of element orders of a finite group

Marius Tărnăuceanu
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Abstract

Let $G$ be a finite group and $H$ be a proper normal subgroup of $G$. In this note, we introduce two new functions $o(G,H)$ and $\psi''(G,H)$ involving the sums of element orders of $G$ and $H$. We prove that they satisfy certain inequalities, with equality if and only if $(G,H)$ is an equal order pair of a particular type.

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Marius Tărnăuceanu. 2026-08-10. Two new functions related to the sum of element orders of a finite group. https://arxiv.org/abs/2608.10035

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