PreprintCC BY 4.0arXiv
Finite groups with large sum of element orders compared to cyclic groups
Abstract
For a finite group G let ψ(G) denote the sum of the orders of elements in G. If G has order n then, by a result of Amiri, Jafarian Amiri and Isaacs, ψ(G)≤ψ(Cn), where Cn is the cyclic group of order n. We determine all finite groups such that ψ(G)≥1/3ψ(Cn).
Related
- Element Orders and Character Codegrees of Finite Groups
- The number of distinct element orders in a finite group
- Finite index rigidity of free-by-cyclic groups
- On Intersection Hypergraph of Finite Non-Cyclic Abelian Groups
- Finite Cyclic Fundamental Groups and Exotic Universal Covers from the Cartwright--Steger Surface
BibTeX
@misc{palfy2026finite,
title = {{Finite groups with large sum of element orders compared to cyclic groups}},
author = {Péter P. Pálfy and Alex D. Simonyi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.27846},
eprint = {2610.27846},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.27846},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Finite groups with large sum of element orders compared to cyclic groups
AU - Péter P. Pálfy
AU - Alex D. Simonyi
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.27846
UR - https://arxiv.org/abs/2610.27846
AB - For a finite group G let ψ(G) denote the sum of the orders of elements in G. If G has order n then, by a result of Amiri, Jafarian Amiri and Isaacs, ψ(G)≤ψ(C_n), where C_n is the cyclic group of order n. We determine all finite groups such that ψ(G)≥1/3ψ(C_n).
ER -