Title Integrable Bi‑Hamiltonian Systems by Jacobi Structure on Real Three‑Dimensional Lie Groups Type of Research Article Keywords Poissonization · Jacobi manifold · Completely integrable Hamiltonian system Abstract By Poissonization of Jacobi structures on real three-dimensional Lie groups G and using the realizations of their Lie algebras, we obtain integrable bi-Hamiltonian systems on G ⊗ ℝ. Researchers Hasan Amirzadeh (First Researcher)، Ghorbanali Haghighatdoost Bonab (Second Researcher)، Adel Rezaei-Aghdam (Third Researcher)