# Changes

If $K$ is the (unique up to isomorphism) finite field of size a prime power $q$, there is a unique quadratic extension $L$ of $K$, and this extension is separable. The extension field is the finite field (unique up to isomorphism) of order $q^2$. The automorphism $\sigma$ is the map $x \mapsto x^q$. The unitary group for this extension may be denoted $U(n,q)$ (the more standard choice) or $U(n,q^2)$ (a less standard choice). Note that due to the multiplicity ambiguity of notation, it is important to understand from context what exactly is meant.