논문KCI 등재
On the number of cyclic subgroups of a finite group
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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 $m.$
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 $m.$
참고문헌 (7)
- M. Hall, "The Theory of Groups" (1963), The Macmillan Company
- "J. Indian Math. Soc", 1965, 155~163
- I. M. Richards, "A remark on the number of cyclic subgroups of a finite group", Amer. Math. Monthly, 91(9), pp.571~572 (1984)
- W. R. Scott, "Group Theory" (1987), Dover Publications, Inc.
- B. Sury, "Some number-theoretic identities from group actions", Rend. Circ. Mat. Palermo, 58(1), pp.99~108 (2009)
- M. Tarnauceanu, "Cyclicity degrees of finite groups", Acta Math. Hungar, 145(2), pp.489~504 (2015)
- L. Toth, "Menon's identity and arithmetical sums representing functions of several vari-ables", Rend. Sem. Mat. Univ. Politec. Torino, 69(1), pp.97~110 (2011)
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