Square-class group of the 2-adic Gaussian field
= Square-class group of the 2-adic Gaussian field
{title2=$\mathbb Q_2(i)^\times/\mathbb Q_2(i)^{\times2}\cong C_2^4$}
The <valuation> contributes one factor $C_2$. The <unit decomposition of the 2-adic Gaussian field> contributes $\mu_4/\mu_4^2\cong C_2$ and the additive quotient $\mathbb Z_2[i]/2\mathbb Z_2[i]\cong C_2^2$. Thus there are sixteen <square classes> and fifteen <quadratic extensions> over this field.