= Ramification groups of the eighth-root cyclotomic extension of the 2-adic field
{title2=$G_0=G_1=C_2^2,\quad G_2=G_3=C_2,\quad G_4=1$}
For $\mathbb Q_2(\zeta_8)/\mathbb Q_2$, the shifted polynomial $(1+T)^4+1$ is <Eisenstein> and $\zeta_8-1$ is a <uniformizer>. The three nonidentity automorphisms have displacement <valuations> two, four and two. Thus the lower breaks are one and three, the upper breaks one and two, and the <different exponent from ramification groups> is eight.
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