Let $p$ be a prime number and $R$ be a Noetherian local ring of characteristic $p$ with residue field $k$. Let $G$ be a finite etale subgroup scheme over $R$ of order $p$. Suppose that the etale $k$-group scheme $G_{s}:=G \times_{S}$Spec$(k)$ is isomorphic to the constant group $\mathbb{Z} / p\mathbb{Z}$. Then is it true that $G$ is itself isomorphic to $\mathbb{Z}/p\mathbb{Z}$ as $R$-groups? (Note that $R$ may not be Henselian).

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