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 <EOS>