When is the restriction map in cohomology an isomorphism? Let $G$ be a group, $H$ one of its normal subgroups and $M$ a $G$-module. If $H^1(G,M)\simeq H^1(H,M)^{G/H}$, can we conclude that $H=G$?

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    $\begingroup$ I wouldn't advise it. $\endgroup$ – Ryan Budney Mar 14 at 15:29
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    $\begingroup$ mathoverflow.net/questions/95036/… $\endgroup$ – Venkataramana Mar 14 at 15:36
  • $\begingroup$ see the above link; there is an exact sequence which tells you that in general, there is a map from $H^1(G,M)$ into $H^1(H,M)^{G/H}$ with kernel $H^1(G/H,M^H)$. $\endgroup$ – Venkataramana Mar 14 at 15:38

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