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Example: Examples of Cyclic Groups
(related to Part: Group Theory)
The following are examples of cyclic groups:
 The integers under addition $(\mathbb Z, + )$ form a cyclic group with the generator $1$ and the generator $1$. There are no other generators.
 Given a positive integer $n$, the $n$th roots of unity in the complex numbers form a cyclic group of order $n$, i.e. the complex exponential function $\exp(2\pi i/n)$ is a generator of this group. Also, if $r$ is relatively prime to $n$, then $\exp(2\pi ir/n)$ is a generator of this group.
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References
Bibliography
 Lang, Serge: "Algebra  Graduate Texts in Mathematics", Springer, 2002, 3rd Edition