In this paper we continue to develop the topological method to get semigroup generators of semi-simple Lie groups. Consider a subset ⊂ G that contains a semi-simple subgroup G 1 of G. If one can show that does not leave invariant a contractible subset on any flag manifold of G, then generates G if Ad ( ) generates a Zariski dense subgroup of the algebraic group Ad (G). 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 ⊂ G.
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