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When the Swedish military decided that 1937 seemed like a pretty good time to be getting some new submachine guns, they arranged to purchase a version of the m/31 Suomi from their Finnish neighbors - which they called the M-37. Since the standard Swedish military pistol (the Husqvarna m/07) was chambered for the 9x20mm Browning Long cartridge, they got a version of the Suomi chambered for that round. It used a rearward-sloping (to prevent rimlock) quad-stand magazine that held 56 rounds.
Shortly after this purchase, however, Sweden bought a number of other foreign-made guns, including Walther HP pistols and German submachine guns in 9mm Parabellum. This was a more powerful and more modern cartridge than the 9x20, and so the followup licensing of Suomis reverted to 9mm Parabellum as well, with the designation M-37/39. While the basic mechanism of these is identical to the Finnish Suomi, they differ in some details, including barrel length, charging handle contour, and stock profile.