Lemma 39.7.6. Let $G$ be a group scheme over a perfect field $k$. Then the reduction $G_{red}$ of $G$ is a closed subgroup scheme of $G$.

Proof. Omitted. Hint: Use that $G_{red} \times _ k G_{red}$ is reduced by Varieties, Lemmas 33.6.3 and 33.6.7. $\square$

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