A [[Cyclic Group|Cyclic]] [[Subgroup]] of some [[Group]] $(G, \circ)$ is a [[Subgroup]] of $G$ that is also a [[Cyclic Group]]. For some element $a\in G$, the [[Cyclic Subgroup]] generated by $a$, denoted as $\braket{a}$ is the [[Set|set]] of all powers of $a$. $\huge \braket{a} = \setbuild{a^{n}}{n\in \Z} $ We define an element $a$ of the group to have a [[Cyclic Subgroup|Group Element Order]] of the size of the [[Set|set]] $\braket{a}$, also denoted as $\op{ord}(a)$.