It is an object of the present invention to provide a rotary electrical device that can be manufactured easily, and which produces a high output torque at low operating speeds. The rotary electrical device comprises: a stator core. The rotary electrical device comprises: a stator core having Z1 stator slots for receiving three-phase windings which generate a rotational magnetic field of p magnetic pole pairs in the stator core, and Z1 permanent magnets being provided in tooth sections fabricated between the stator slots around the stator core; and a rotor core having Z2 permanent magnets being provided around the rotor core; wherein Z1, Z2 and p are related by an expression Z2=Z1±p, and direction of magnetic poles of all permanent magnets are aligned identically in a radial direction.