| http://www.w3.org/ns/prov#value | - Then the map from $H^1(G;\mathbb{F}_p)=\mathbb{F}_p^2$ to $H^1(H;\mathbb{F}_p)=\mathbb{F}_p$ is the zero map (this is a good exercise), so $ ext{res}$ is not surjective. (For a related topological example, let $T^1\Sigma_g$ be the unit tangent bundle of an orientable surface of genus $g>1$, let $G=\pi_1(T^1\Sigma_g)$, and let $H\approx \mathbb{Z}$ be its center.)
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