Cyclic Group/Examples
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Examples of Cyclic Groups
Subgroup of $\struct {\R_{\ne 0}, \times}$ Generated by $2$
Consider the multiplicative group of real numbers $\struct {\R_{\ne 0}, \times}$.
Consider the subgroup $\gen 2$ of $\struct {\R_{\ne 0}, \times}$ generated by $2$.
Then $\gen 2$ is an infinite cyclic group.
Subgroup of $\struct {\C_{\ne 0}, \times}$ Generated by $i$
Consider the multiplicative group of complex numbers $\struct {\C_{\ne 0}, \times}$.
Consider the subgroup $\gen i$ of $\struct {\C_{\ne 0}, \times}$ generated by $i$.
Then $\gen i$ is an (finite) cyclic group of order $4$.