A compact, light permanent magnet motor with low torque pulsations is obtained by reducing a cogging torque resulting from variations at the end of a rotor, such as an error in attachment position and a variation in magnet characteristic of the permanent magnets. A permanent magnet rotating electrical machine includes a rotor and a stator, a stator core provided with slots in which to store an armature winding wire wound around the teeth, and supplemental grooves provided to the teeth in portions opposing the rotor in an axial direction of the stator core. The supplemental grooves are provided to the stator in a part in the axial direction of the stator core, and that let P be the number of the magnetic poles (the number of poles) and S be the number of the slots (the number of slots), then a relation, 0.75