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Maximal compact subgroup of p-adic lie groups

Let $k$ be a number field and $S$ be a finite set of places of $k$. Let $G$ be a connected semisimple algebraic group over $k$. Let $k_S=\prod_{v\in S}k_v$ where $k_v$ is the completion of $k$ at $v$.

Question: Is maximal compact subgroup of $G(k_S)$ unique up to conjugation? If it is not unique, are there finitely many of them up to conjugation?

ronggang
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