Transmission for a vehicle, and power train having such a transmission

A transmission (3) for a power train (2) of a vehicle (1), comprising:

• an input shaft (4);
• a first output shaft (5);
• a second output shaft (6);
• and
• a differential (7) operatively arranged between the input shaft (4) and the first and second output shafts (5, 6), the differential (7) comprising a first planetary gear set (8) and a second planetary gear set (9), the first planetary gear set (8) comprising a first gear set element, a second gear set element, and a third gear set element, a first output torque being at least indirectly transmittable onto the first output shaft (5) by the first planetary gear set (8), the second planetary gear set (9) comprising a first gear set element, a second gear set element, and a third gear set element, the second planetary gear set (9) operatively connected to the first planetary gear set (8), a support torque of the first planetary gear set (8) being convertible in the second planetary gear set (9) such that a second output torque, which corresponds to the first output torque, is transmittable onto the second output shaft (6),
• wherein the first gear set element of the first planetary gear set (8) is connected to the input shaft (4) for conjoint rotation, the second gear set element of the first planetary gear set (8) is connected to the first output shaft (5) for conjoint rotation via a spline (24) that includes an inner toothing (10) on the second gear set element of the first planetary gear set (8) and an outer toothing (12) on the first output shaft (5), a third gear set element of the first planetary gear set (8) is at least indirectly connected to the first gear set element of the second planetary gear set (9) for conjoint rotation, the second gear set element of the second planetary gear set (9) is connected to a stationary component (27) for conjoint rotation, the third gear set element of the second planetary gear set (9) is at least indirectly connected to the second output shaft (6) for conjoint rotation,
• wherein at least one first duct (14) for axial passage of lubricant is formed between the inner toothing (10) and the outer toothing (12)
• wherein an axial portion (19) of the second gear set element of the first planetary gear set (8) is arranged radially between the first output shaft (5) and the second output shaft (6), and
• wherein at least one second duct (23) for the axial passage of lubricant is formed on an inner circumference (21) of the second output shaft (6) proximate the axial portion (19) of the second gear set element of the first planetary gear set (8).