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

2020/01/20 by Marius Tărnăuceanu, Tărnăuceanu, Marius
Engineering · Mathematics · #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications #Group Theory (math.GR) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2001.07275

openalex publication_date 2020/01/20 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

Let G be a finite group and let \ψ(G) denote the sum of element orders\nof G. It is well-known that the maximum value of \φ on the set of\ngroups of order n, where n is a positive integer, will occur at the cyclic\ngroup C_n. For nilpotent groups, we prove a natural generalization of this\nresult, obtained by replacing the element orders of G with the element orders\nrelative to a certain subgroup H of G.\n

Related

• A result on certain sums of element orders in finite groups
• A criterion for nilpotency of a finite group by the sum of element orders
• An exact upper bound for sums of element orders in non-cyclic finite groups
• An exact upper bound for the sum of powers of element orders in non-cyclic finite groups
• On the Sum of Element Orders in Finite Abelian Groups