Mathematical study reveals novel bounding inequalities for element order sums across finite groups, indicating precise criteria for equal order pairs.
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: see text]. We prove that they satisfy certain inequalities, with equality if and only if [Formula: see text] is an equal order pair of a particular type.
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Marius Tărnăuceanu (2026) studied this question.
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