The invention relates to an electric propulsion unit (10) and torque transmission group (11) for operating the rear wheel (13) of an electric scooter (1) with body (2) of the step-through type and with upright sitting portion (6). The electric propulsion unit (10) comprises at least one synchronous electric motor (30) of the type comprising internal stator (32) and external rotor (29) with a cup-shaped form rotating on a fixed shaft (33) rigid with the stator (32); the motor is installed in a barycentric position substantially at the base of the upright sitting portion (6) with the fixed shaft (33) transverse to the longitudinal axis (X-X) of the scooter (2), and the transmission group (11) comprises at least one first and one second reduction stage (24, 26).