Let $G$ be an algebraic group defined over a char 0
local field $k$. Following Borel and Tits (73) we define
the group $G^+(k)$ or $G^+$ by the subgroup of $G(k)$
generated by the unipotent elements of $G(k)$. 

Suppose $G$ is gegerated by a finite set of unipotent 
$k$-sugroups, say $U_1,\cdots, U_n$. Is it true that 
the group generated by $U_1(k), \cdots, U_n(k)$ is 
$G^+$? 

I feel the answer is positive but do not know how to prove it.
It seems that the ideas of the original paper of Borel and Tits can 
help, but I still do not read French (which I always plan to learn) yet.