What does this research mean for the field?

Finite groups G can be completely determined such that the difference in subgroup orders divides the difference in the sum of element orders for all subgroups K ≤ H ≤ G. Novelty: ClaimNovelty.INCREMENTAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

To classify finite groups in which the difference in subgroup orders divides the difference in the sums of element orders for all nested subgroups.

September 3, 2026Asian-European Journal of MathematicsOpen Access

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

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To classify finite groups in which the difference in subgroup orders divides the difference in the sums of element orders for all nested subgroups.
Analyzed the divisibility relationship between subgroup order differences (|H| - |K|) and element order sum differences (ψ(H) - ψ(K)) for all subgroups K ≤ H ≤ G.
Formulated and evaluated two weaker alternative divisibility conditions on subgroup structures.
Identified and classified the specific families of finite groups G that satisfy the primary subgroup divisibility criterion.
Characterized structural behaviors under two weaker variants of the divisibility condition.

Implication

Theoretical analysis determines subgroup divisibility relations for element order sums in finite groups, uncovering structural classification constraints.

Abstract

Given a finite group G, we denote by [Formula: see text](G) the sum of element orders of G. In this note, we determine finite groups G such that [Formula: see text]H[Formula: see text] – [Formula: see text]K[Formula: see text] divides [Formula: see text](H) – [Formula: see text](K) for all subgroups K ≤ H ≤ G. Two weaker conditions are also proposed.

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Cite This Study

Marius Tărnăuceanu (2026) studied this question.

synapsesocial.com/papers/6a9934b4636c6408cfa7c684 https://doi.org/10.1142/s1793557126501093

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Implication

Theoretical analysis determines subgroup divisibility relations for element order sums in finite groups, uncovering structural classification constraints.

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

Key Points

Implication

Abstract

Discussion

Cite This Study

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

Key Points

Implication

Abstract

Discussion

Cite This Study

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