Let $G$ be a reductive group over a $p$-adic field $k$, $S \subset G$ a maximal $k$-split torus, $\Phi(G,S)$ the relative root system and $\Delta$ a basis of $\Phi$.

There is a group homomorphism : $$S(k) \to \mathbb{Z}^{\Delta}, s \mapsto (\mathrm{ord_p} \alpha(s))_{\alpha \in \Delta}$$ with finite cokernel and kernel equal to $S_0 (Z(k) \cap S(k))$ where $S_0 \subset S(k)$ is the maximal compact subgroup and $Z$ the center of $G$.

This is used in many papers (e.g. Tit's "Reductive groups over local fields") but I could not find a reference for the proof.

`$S$`

is just a product of multiplicative groups, maybe it's easy to generalize to higher rank. In any case, Tits himself had some early announcements and expositions before the more technical Bruhat-Tits papers appeared. I'll take a closer look. – Jim Humphreys May 30 '13 at 22:45