Marius Tărnăuceanu

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

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](...

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

Let [Formula: see text] be a finite group and [Formula: see text] be a proper normal subgroup of [Formula: see text]. In this note, we introduce two new functions [Formula: see text] and [Formula: see text] involving the sums of element orders of [Formula: see text] and [Formula:...