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[en] In this short note we summarize recent results obtained by the renormalization group approach to quasi-one-dimensional electron gas model. The approach is applied to the Bechgaard salts series (TMTSF)2X and the results are shown to give a satisfactory account of the interdependence between antiferromagnetism and superconductivity featured by their phase diagram, the anomalous enhancement of the nuclear relaxation and the electron-electron scattering rate under pressure.