Bulletin of the
Korean Mathematical Society
BKMS

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

Article

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Bull. Korean Math. Soc. 2017; 54(6): 2141-2147

Online first article July 26, 2017      Printed November 30, 2017

https://doi.org/10.4134/BKMS.b160783

Copyright © The Korean Mathematical Society.

On the number of cyclic subgroups of a finite group

Mohammad Hossein Jafari, Ali Reza Madadi

University of Tabriz, University of Tabriz

Abstract

Let $G$ be a finite group and $m$ a divisor of $|G|.$ We prove that $G$ has at least $\tau(m)$ cyclic subgroups whose orders divide $m$, where $\tau(m)$ is the number of divisors of $m.$

Keywords: cyclic subgroups, Sylow subgroups, arithmetic functions

MSC numbers: 20D15, 20D20, 11A25