Abstract: A power transmission system for an aircraft turbine engine including a speed reducer including a ring gear that is able to rotate about an axis X, formed from half-rings having annular flanges clamped together by first fastener. The reducer includes an annular channel for recovering centrifuged oil, having a U-shaped cross section, extending around the flanges, this channel being formed by an axial assembly of at least two parts and forming a fairing for the flanges and the first fastener intended to limit aerodynamic disturbances.