A permanent magnet electric machine such as, for example, a motor or generator, including a permanent magnet field member, an armature having salient magnetic poles and armature windings. A greatest common division of the number of magnetic poles of the field member and the salient magnetic poles having the armature windings differs from the number of magnetic poles. A group of grooves is formed between the salient magnetic poles having an interval of 2/3M.pi., with M being an integer which is not a multiple of three. To reduce the occurrence of cogging torque, auxiliary grooves are provided on the surface of the salient poles at positions which are spaced apart from positions of the grooves by (.pi./3)K+(.pi./6), in terms of electrical angle, with K being an integer.