  Let $G$ be a semisimple linear algebraic group over a field $k$ and let
$G^+(k)$ be the subgroup generated by the subgroups $R_u(Q)(k)$, where $Q$
ranges over all the minimal $k$-parabolic subgroups $Q$ of $G$. We prove that
if $G^+(k)$ is bounded then it is uniformly bounded. Under extra assumptions we
get explicit bounds for $\Delta(G^+(k))$: we prove that if $k$ is algebraically
closed then $\Delta(G^+(k))\leq 4\, {\rm rank}\,G$, and if $G$ is split over
$k$ then $\Delta(G^+(k))\leq 28\, {\rm rank}\,G$. We deduce some analogous
results for real and complex semisimple Lie groups.
