Sums of element orders in groups of odd order

Marcel Herzog, Patrizia Longobardi, Mercede Maj*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

For a finite group G, let ψ(G) denote the sum of element orders of G. If n is a positive integer let Cn be the cyclic group of order n. It is known that ψ(Cn) is the maximum value of ψ on the set of groups of order n, and ψ(G) = ψ(Cn) if and only if G is cyclic of order n. In this paper, we investigate the second largest value of ψ on the set of groups of order n and the structure of groups G of order n with this value of ψ(G) when n is odd.

Original languageEnglish
Pages (from-to)1049-1063
Number of pages15
JournalInternational Journal of Algebra and Computation
Volume31
Issue number6
DOIs
StatePublished - Sep 2021

Funding

FundersFunder number
Istituto Nazionale di Alta Matematica "Francesco Severi"

    Keywords

    • Group element orders
    • finite groups

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