= Inflation-restriction exact sequence
{title2=$0\to H^1(G/N,M^N)\to H^1(G,M)\to H^1(N,M)^{G/N}$}
For a normal subgroup $N$ of $G$ and a $G$-module $M$, the low-degree exact sequence begins $0\to H^1(G/N,M^N)\to H^1(G,M)\to H^1(N,M)^{G/N}\to H^2(G/N,M^N)$. The first map inflates cocycles along $G\to G/N$; the second restricts them. If the restriction is trivial, subtract a coboundary to make the cocycle vanish on $N$ and descend to the quotient. Thus for a finite Galois extension, the kernel of restriction on <Galois cohomology> with finite coefficients is finite.
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