Square-class group of a p-adic field
= Square-class group of a p-adic field
{title2=$\mathbb Q_p^\times/(\mathbb Q_p^\times)^2$}
For odd $p$, parity of <valuation> and the <square class> of the unit residue give a <group> $C_2\times C_2$, represented by $1,u,p,pu$ for a unit $u$ with nonsquare residue. For $p=2$, <valuation> parity and unit residue modulo eight give $C_2^3$, with generators $-1,5,2$. The unit criteria follow from the <Hensel lemma>, using its strong derivative version for $p=2$.