Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2024; 61(3): 611-619

Online first article March 20, 2024      Printed May 31, 2024

https://doi.org/10.4134/BKMS.b230266

Copyright © The Korean Mathematical Society.

A density theorem related to Dihedral groups

Arya Chandran, Kesavan Vishnu Namboothiri, Vinod Sivadasan

Chinmaya Vishwa Vidyapeeth, Ernakulam; Department of Collegiate Education; Thiruvananthapuram

Abstract

For a finite group $G$, let $\psi(G)$ denote the sum of element orders of $G$. If $\psi^{\prime\prime}(G)=\frac{\psi(G)}{|G|^2} $, we show here that the image of $\psi^{\prime\prime}$ on the class of all Dihedral groups whose order is twice a composite number greater than 4 is dense in $[0,\frac{1}{4}]$. We also derive some properties of $\psi^{\prime\prime}$ on the class of all dihedral groups whose order is twice a prime number.

Keywords: Sum of element orders, dihedral groups

MSC numbers: Primary 20D30; Secondary 20E34, 40A05, 03E20

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