  In this paper we continue to develop the topological method started in
Santos-San Martin \cite{ariasm} to get semigroup generators of semi-simple Lie
groups. Consider a subset $\Gamma \subset G$ that contains a semi-simple
subgroup $G_{1}$ of $G$. Then $\Gamma $ generates $G$ if $\mathrm{Ad}\left(
\Gamma \right) $ generates a Zariski dense subgroup of the algebraic group
$\mathrm{Ad}\left( G\right) $. The proof is reduced to check that some specific
closed orbits of $G_{1}$ in the flag manifolds of $G$ are not trivial in the
sense of algebraic topology. Here, we consider three different cases of
semi-simple Lie groups $G$ and subgroups $G_{1}\subset G$.
