A machine element designed for transferring a force and/or a torque and also for measuring the force or the torque to be transferred, as well as to an arrangement for measuring a force and/or a torque having such a machine element. A method for producing the machine element is also provided. The machine element according to the invention has a primary sensor for measuring the force to be transferred or the torque to be transferred and this sensor has a permanent magnetization. A measurable magnetic field occurring outside of the machine element is caused by the permanent magnetization and also by the force and/or by the torque. The permanent magnetization extends along a closed magnetization path. The permanent magnetization is formed in a surface layer of the machine element that has a greater magnetic permeability than at least the sections of the machine element located under the surface layer.