Abstract: It is proved here that the subsemigroup of positive matrices in Sl(n, R) is maximal connected. Also, let g be a simple non-compact Lie algebra and k Cg a maximal compactly embedded subalgebra. If G is a connected Lie group with Lie algebra g, and K the connected subgroup whose Lie subalgebra is k, then any coset Kg,g K, generates G as a semigroup. Therefore K is maximal as a subsemigroup of G. This result was already obtained by Neeb [3], through different methods Ver menos