Addendum to “A generalization of a result on the sum of element orders of a finite group”

Abstract

Abstract Let G be a group of order n and H be a subgroup of order m of G. Denote by ψ H (G) the sum of element orders relative to H of G. It is known that if G is nilpotent, then ψ H ( G ) ≤ ψ H m ( C n ) $ \psi_H(G) \leq\psi_{H_m}(C_n) $ , where H m is the unique subgroup of order m of C n . In this note, we show that this inequality does not hold for infinitely many finite solvable groups.