In this paper, we establish the relation between the concept of control subgroups and the class of graded birational algebras. Actually, we prove that if R = ⊕ σ ∈ G R σ is a strongly G -graded ring and H ⊲ G , then the embedding i : R ( H ) ↪ R , where R ( H ) = ⊕ σ ∈ H R σ , is a Zariski extension if and only if H controls the filter ℒ ( R − P ) for every prime ideal P in an open set of the Zariski topology on R . This enables us to relate certain ideals of R and R ( H ) up to radical.