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Let $G$ be a group, and let $H$ be a subgroup of $G$. Suppose that $E$ is an injective module over $\mathbb{Z}G$. Then I think that, as a consequence of Baer's criterion, $E$ is also an injective module over $\mathbb{Z}H$.

If I am right, then the above property shall be well-known, but I am not aware of any reference. Could anyone provide a reference or disprove the statement? Thanks!

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