Cyclic group:Z16

Definition
The cyclic group of order sixteen, denoted $$C_{16}, \mathbb{Z}_{16}$$ or sometimes $$\mathbb{Z}/16\mathbb{Z}$$, is the cyclic group having $$16$$ elements. In other words, it is the quotient of the group of integers $$\mathbb{Z}$$ by the subgroup $$16\mathbb{Z}$$ of multiples of $$16$$.

It is given by the presentation:

$$\langle x \mid x^{16} = e \rangle$$

where $$e$$ is the identity element.