Definition:Multiplicative Group of Reduced Residues

Definition
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 $m$.

Also known as
Some sources refer to this group merely as the multiplicative group modulo $m$, glossing over the fact that the underlying set is actually a reduced residue system.

Also see

 * Reduced Residue System under Multiplication forms Abelian Group