A remark on a theorem of J. Tits

Let $G$ be a rank two Chevalley group and $\Gamma$ be the corresponding Moufang polygon. J. Tits proved that $G$ is the universal completion of the amalgam formed by three subgroups of $G$: the stabilizer $P_1$of a point $a$ of $\Gamma$, the stabilizer $P_2$ of a line $\ell$ incident with $a$, and the stabilizer $N$ of an apartment $A$ passing through $a$ and $\ell$. We prove a slightly stronger result, in which the exact structure of $N$ is not required. Our result can be used in conjunction with the ``weak $BN$-pair" theorem of Delgado and Stellmacher in order to identify subgroups of finite groups generated by minimal parabolics.