Question

What is the order of each group:

(e).$U_{18}$

Short answer

The order of $U_{18}$is $6$.

Step-by-step solution

Order of a group

The order of group $G$is defined as the number of elements in the group.

Definition of group Un

Let us denote the multiplicative group of units in ${\mathrm{\mathbb{Z}}}_n$ by $U_n$.

Then, $U_n$consists of all $a\in {\mathrm{\mathbb{Z}}}_n$, such that $\left(a,n\right)=1$(when a is considered as an ordinary integer).

Conclusion

Clearly, by definition, $U_{18}$ is given by:

$U_{18}=\left\{1,5,7,11,13,17\right\}$.

So, the order of $U_{18}$ is 6.