A generalization of a result on the sum of element orders of a finite group

Publication date: 20 January 2020

Abstract: Let

G

be a finite group and let

p s i (G)

denote the sum of element orders of

G

. It is well-known that the maximum value of

v a r p h i

on the set of groups of order

n

, where

n

is a positive integer, will occur at the cyclic group

C_{n}

. For nilpotent groups, we prove a natural generalization of this result, obtained by replacing the element orders of

G

with the element orders relative to a certain subgroup

H

of

G

.

This page was built for publication: A generalization of a result on the sum of element orders of a finite group