Square-class group of a field
= Square-class group of a field
{title2=$K^{\times}/(K^{\times})^2$}
The square-class group identifies two nonzero elements of a <field> when their quotient is a square. Multiplication makes it an <abelian group> of exponent two, hence a <vector space> over $\mathbb F_2$. It records quadratic extensions and the images of <Kummer theory> for $n=2$.