\begin{definition}[Definition:Multiplicative Group of Reduced Residues]
Let $m \in \Z_{> 0}$ be a (strictly) positive integer.
Let $\Z'_m$ denote the reduced residue system modulo $m$.
Consider the algebraic structure:
:$\struct {\Z'_m, \times_m}$
where $\times_m$ denotes multiplication modulo $m$.
Then $\struct {\Z'_m, \times_m}$ is referred to as '''the multiplicative group of reduced residues modulo $m$'''.
\end{definition}