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Since $i$ is a map of rings, if $\tau$ were a map of rings, then $\tau\circ i$ would also be a map of rings. But the latter maps $1\in H^0(G_2)$ to $[G_2:G_1]$ which, in general, is nornot$1$.
Since $i$ is a map of rings, if $\tau$ were a map of rings, then $\tau\circ i$ would also be a map of rings. But the latter maps $1\in H^0(G_2)$ to $[G_2:G_1]$ which, in general, is nor$1$.
Since $i$ is a map of rings, if $\tau$ were a map of rings, then $\tau\circ i$ would also be a map of rings. But the latter maps $1\in H^0(G_2)$ to $[G_2:G_1]$ which, in general, is not$1$.
Since $i$ is a map of rings, if $\tau$ were a map of rings, then $\tau\circ i$ would also be a map of rings. But the latter maps $1\in H^0(G_2)$ to $[G_2:G_1]$ which, in general, is nor $1$.
