Currently, I am reading Rohrlich's article "Elliptic Curves and the Weil-Deligne Group" and got stuck in the beginning already.
Namely, let $k$ be a finite field of characteristic $p$ and cardinality $q$ and let $\bar{k}$ denote an algebraic closure of $k$. Then it is said that for an positive integer $n$ then there is a unique subfield $k_n$ of $\bar{k}$ of degree $n$ over $k$.
Could you explain me why it exists and why this is a unique subfield? Thank you.