First Lubin–Tate torsion fields for the p-adic numbers
= First Lubin–Tate torsion fields for the p-adic numbers
The two Lubin–Tate series $(1+X)^p-1$ and $X^p+pX$ for $\mathbb Q_p$ have respective nonzero $p$-torsion points $\zeta_p-1$ and the roots of $X^{p-1}=-p$. A <Lubin–Tate change of series> identifies their torsion fields, so
$$
\mathbb Q_p(\zeta_p)=\mathbb Q_p(\sqrt[p-1]{-p}).
$$