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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, thenψ  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.

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