A low-pressure compressor for a turbine engine, such as an aircraft turbojet engine includes a rotor with two rows of rotor blades between which two annular ribs are positioned; and one annular row of stator blades between the rotor blades. An internal shroud is connected to the stator blades. The internal shroud includes abradable material collaborating with the annular ribs, and annular teeth made of an abradable material and which extend radially towards the rotor, so as to provide sealing. The system may be used in a method for manufacturing a bypass turbojet engine compressor.