commutator

(kŏmˈyə-tāˌtər)

1. A cylindrical arrangement of insulated metal bars connected to the coils of a direct-current electric motor or generator, providing a unidirectional current from the generator or a reversal of current into the coils of the motor.
2. Mathematics In a commutative or noncommutative group, an element of the form ghg^-1h^-1 where g and h are elements of the group. If g and h commute, the commutator is the identity element.