The paper first shows that for a path connected topological group acting analytically on a complex manifold M M , the induced action on the cohomology groups of antiholomorphic forms on M M is trivial. By the same method it then shows that the cohomology groups of complex { ker ⁡ ∂ p , ∗ } \{ \ker {\partial ^{p,\ast }}\} can be injected into the Dolbeault cohomology groups.