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The Compact Muon Solenoid (CMS) is one of the general-purpose detectors to be provided for the LHC project at CERN. The design field of the CMS superconducting magnet is 4 T, the magnetic length is 12.5 m and the free bore is 6 m. Almost all large indirectly cooled solenoids constructed to date (e.g., Zeus, Aleph, Delphi, Finuda, Babar) comprise Al-alloy mandrels fabricated by welding together plates bent to the correct radius. The external cylinder of CMS will consist of five modules having an inner diameter of 6.8 m, a thickness of 50 mm and an individual length of 2.5 m. It will be manufactured by bending and welding thick plates (75 mm) of the strain hardened aluminum alloy EN AW-5083-H321. The required high geometrical tolerances and mechanical strength (a yield strength of 209 MPa at 4.2 K) impose a critical appraisal of the design, the fabrication techniques, the welding procedures and the quality controls. The thick flanges at both ends of each module will be fabricated as seamless rolled rings, circumferentially welded to the body of the modules. The developed procedures and manufacturing methods will be validated by the construction of a prototype mandrel of full diameter and reduced length (670 mm).