Abstract
Abstract Let $G$ be a reductive group over a non-archimedean local field $k$. We provide necessary conditions and sufficient conditions for all tori of $G$ to split over a tamely ramified extension of $k$. We then show the existence of good semisimple elements in every Moy–Prasad filtration coset of the group $G(k)$ and its Lie algebra, assuming the above sufficient conditions are met.
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