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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 $m.$
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참고문헌 (7)
참고문헌 신청
B. Sury / 2009 / Some number-theoretic identities from group actions / Rend. Circ. Mat. Palermo 58 (1) : 99 ~ 108
I. M. Richards / 1984 / A remark on the number of cyclic subgroups of a finite group / Amer. Math. Monthly 91 (9) : 571 ~ 572
L. Toth / 2011 / Menon's identity and arithmetical sums representing functions of several vari-ables / Rend. Sem. Mat. Univ. Politec. Torino 69 (1) : 97 ~ 110
M. Hall / 1963 / The Theory of Groups / The Macmillan Company
M. Tarnauceanu / 2015 / Cyclicity degrees of finite groups / Acta Math. Hungar 145 (2) : 489 ~ 504
I. M. Richards / 1984 / A remark on the number of cyclic subgroups of a finite group / Amer. Math. Monthly 91 (9) : 571 ~ 572
L. Toth / 2011 / Menon's identity and arithmetical sums representing functions of several vari-ables / Rend. Sem. Mat. Univ. Politec. Torino 69 (1) : 97 ~ 110
M. Hall / 1963 / The Theory of Groups / The Macmillan Company
M. Tarnauceanu / 2015 / Cyclicity degrees of finite groups / Acta Math. Hungar 145 (2) : 489 ~ 504
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