A laundry washing machine comprising: - a washing tub in which washing/rinsing liquid may be loaded; - a drain duct for discharging outside the machine washing/rinsing liquid drawn from the washing tub; - a recirculation conduit for circulating washing/rinsing liquid drawn from the washing tub back into the washing tub; - a pump operable to selectively cause washing/rinsing liquid drawn from the washing tub to be discharged via said drain duct or to be circulated via said recirculation conduit, said pump comprising: a) a pump body comprising a pump chamber housing an impeller, the pump chamber being adapted to receive washing/rinsing liquid drawn from said washing tub, and b) a diverter element rotatably arranged in said pump chamber and movable by rotation between a first position in which said diverter element causes washing/rinsing liquid in the pump chamber to be diverted to said drain duct, and a second position, in which said diverter element causes washing/rinsing liquid in the pump chamber to be diverted to said recirculation conduit; - the laundry washing machine further comprises an actuator system including a rotatable transmission element rotatably fitted around an external surface of the pump body, said rotatable transmission element being magnetically coupled to said diverter element so that the rotation of the rotatable transmission element with respect to the pump body causes a corresponding rotation of the diverter element inside the pump chamber. - a washing tub in which washing/rinsing liquid may be loaded; - a drain duct for discharging outside the machine washing/rinsing liquid drawn from the washing tub; - a recirculation conduit for circulating washing/rinsing liquid drawn from the washing tub back into the washing tub; - a pump operable to selectively cause washing/rinsing liquid drawn from the washing tub to be discharged via said drain duct or to be circulated via said recirculation conduit, said pump comprising: a) a pump body comprising a pump chamber housing an impeller, the pump chamber being adapted to receive washing/rinsing liquid drawn from said washing tub, and b) a diverter element rotatably arranged in said pump chamber and movable by rotation between a first position in which said diverter element causes washing/rinsing liquid in the pump chamber to be diverted to said drain duct, and a second position, in which said diverter element causes washing/rinsing liquid in the pump chamber to be diverted to said recirculation conduit; a) a pump body comprising a pump chamber housing an impeller, the pump chamber being adapted to receive washing/rinsing liquid drawn from said washing tub, and b) a diverter element rotatably arranged in said pump chamber and movable by rotation between a first position in which said diverter element causes washing/rinsing liquid in the pump chamber to be diverted to said drain duct, and a second position, in which said diverter element causes washing/rinsing liquid in the pump chamber to be diverted to said recirculation conduit; - the laundry washing machine further comprises an actuator system including a rotatable transmission element rotatably fitted around an external surface of the pump body, said rotatable transmission element being magnetically coupled to said diverter element so that the rotation of the rotatable transmission element with respect to the pump body causes a corresponding rotation of the diverter element inside the pump chamber.