Multiplicative group of a finite field is cyclic

Statement
Suppose $$k$$ is a finite field. Let $$k^\times$$ denote the multiplicative group of $$k$$. Then, $$k^\times$$ is a cyclic group.

Facts used

 * 1) uses::Multiplicative group of a field implies every finite subgroup is cyclic

Proof
The statement follows directly from fact (1).