I just so happen to own a Remington UMC model 10, actually it is pre model 10, they did not name this the model 10 until 1911 I believe. Mine actually has the dates 1903 and 1905 on it. But to get to your answer it stands for UNION METALLIC CARTRIDGE.
1913
1920
1913
Made in 1908
Early 1909
Are you sure it's an auto and not a pump action, it sounds like the predecessor to the Remington Model 10.
What Model 51 pistol or a rifle and what model?
Union Metallic Cartridge, it's part of the Remington Company
With that type of serial number Tue gun can't be that old. Probably 50
Union Metalic Cartridge Co. is a division of Remington UMC purchased Remington Arms Co in 1912 and became Remington Arms UMC.
1913 (early)
1917