A permanent magnet synchronous machine comprising: a stator equipped with a stator coil wound on a plurality of teeth; and a rotor equipped with a plurality of permanent magnets and a plurality of permanent magnet housing holes for housing the permanent magnets in a peripheral direction, the rotor being provided with a plurality of magnetic poles disposed along a peripheral direction, wherein the permanent magnet synchronous machine is characterized in that a ratio τm/τp of an open angle τp of the magnetic pole to an open angle τm of the permanent magnet satisfies the mathematical expression 1; and a reluctance torque ratio α defined by the mathematical expression 2 using stator coil interlinkage magnetic fluxes Wp by the permanent magnet, direct-axis inductance Ld, and quadrature-axis inductance Lq respectively when current I (Arms) is electrified is 0.60 or more, wherein a cross-section area of a core peripheral part configured by outer sides in a diametric direction of the permanent magnet and a peripheral end of the rotor and cut by the open angle τm of the permanent magnet is made smaller than cross-section area of the permanent magnet housing hole, wherein the permanent magnet housing hole and one side of the permanent magnet housing hole extended in the peripheral direction are perpendicular to a magnetic pole central axis of the permanent magnet configuring one pole, characterized in that the permanent magnet is arranged in a state in which the permanent magnet is divided into a plurality of pieces in the circumferential direction [Mathematical expression 1] 0.5 ≤ τ m τ p ≤ 0.63 [Mathematical expression 2] α = L q − L d Ψ p ⋅ I rms 2 a stator equipped with a stator coil wound on a plurality of teeth; and a rotor equipped with a plurality of permanent magnets and a plurality of permanent magnet housing holes for housing the permanent magnets in a peripheral direction, the rotor being provided with a plurality of magnetic poles disposed along a peripheral direction, wherein the permanent magnet synchronous machine is characterized in that a ratio τm/τp of an open angle τp of the magnetic pole to an open angle τm of the permanent magnet satisfies the mathematical expression 1; and a reluctance torque ratio α defined by the mathematical expression 2 using stator coil interlinkage magnetic fluxes Wp by the permanent magnet, direct-axis inductance Ld, and quadrature-axis inductance Lq respectively when current I (Arms) is electrified is 0.60 or more, wherein a cross-section area of a core peripheral part configured by outer sides in a diametric direction of the permanent magnet and a peripheral end of the rotor and cut by the open angle τm of the permanent magnet is made smaller than cross-section area of the permanent magnet housing hole, wherein the permanent magnet housing hole and one side of the permanent magnet housing hole extended in the peripheral direction are perpendicular to a magnetic pole central axis of the permanent magnet configuring one pole, characterized in that the permanent magnet is arranged in a state in which the permanent magnet is divided into a plurality of pieces in the circumferential direction [Mathematical expression 1] 0.5 ≤ τ m τ p ≤ 0.63 [Mathematical expression 2] α = L q − L d Ψ p ⋅ I rms 2