Ramification groups of the splitting field of Xp minus p over the p-adic numbers
= Ramification groups of the splitting field of Xp minus p over the p-adic numbers
{title2=$\mathbb Q_p(\zeta_p,\sqrt[p]{p})/\mathbb Q_p$}
For odd $p$, the splitting field $K=\mathbb Q_p(\zeta_p,\sqrt[p]{p})$ is totally ramified of degree $p(p-1)$. With
$$
\varpi=\frac{\zeta_p-1}{\sqrt[p]{p}},
$$
the lower ramification groups are
$$
G_0=\operatorname{Gal}(K/\mathbb Q_p),\qquad
G_i\cong\mathbb Z/p\mathbb Z\ (1\leq i\leq p),\qquad
G_i=1\ (i\geq p+1).
$$