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