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 On the number of cyclic subgroups of a finite group Bull. Korean Math. Soc. 2017 Vol. 54, No. 6, 2141-2147 https://doi.org/10.4134/BKMS.b160783Published online November 30, 2017 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 Downloads: Full-text PDF