A Group Presentation for Zn

# A Group Presentation for Zn

Let $\mathbb{Z}_n$ denote the group of integers modulo $n$ with the operator of addition. We represent the elements of this group by:

(1)\begin{align} \quad \mathbb{Z}_n = \{ 0, 1, ..., n - 1 \} \end{align}

Then a group presentation for $\mathbb{Z}_n$ is:

(2)\begin{align} \quad \langle a : a^n = 1 \rangle \end{align}