For a finite group with a normal subgroup, two new relative invariants of element orders are shown to lie on opposite sides of the corresponding invariants of the quotient, with equality cases characterized as equal order pairs.
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Two new functions related to the sum of element orders of a finite group
For a finite group with a normal subgroup, two new relative invariants of element orders are shown to lie on opposite sides of the corresponding invariants of the quotient, with equality cases characterized as equal order pairs.