\begin{definition}[Definition:Cyclic Group/Notation]
A '''cyclic group''' with $n$ elements is often denoted $C_n$.
Some sources use the notation $\sqbrk g$ or $\gen g$ to denote the '''cyclic group''' generated by $g$.
From Integers Modulo m under Addition form Cyclic Group, $\struct {\Z_m, +_m}$ is a '''cyclic group'''.
Thus $\struct {\Z_m, +_m}$ often taken as the archetypal example of a '''cyclic group''', and the notation $\Z_m$ is used.
This is justified as, from Cyclic Groups of Same Order are Isomorphic, $\Z_m$ is isomorphic to $C_m$.
In certain contexts $\Z_m$ is particularly useful, as it allows results about '''cyclic groups''' to be demonstrated using number theoretical techniques.
\end{definition}