commutator
nounEtymology Back-formation from commutation (in the late 19th century), as is commutate (verb) too.
1
An electrical switch, in a generator or motor, that periodically reverses the direction of an electric current.
2
Group theory, Mathematics, Sciences A binary map in a given group G, given by [g, h] = ghg⁻¹h⁻¹, where g and h are elements of G, which yields the group's identity if and only if the group operation commutes for g and h.
3
A binary map in a given ring R, given by [a, b] = ab − ba, where a and b are elements of R, which yields the ring's zero element if and only if the multiplication operation commutes for a and b.
- Derived terms
- anticommutator, commutator length, commutatorless, commutator subgroup, multicommutator, self-commutator, subcommutator
- Related terms
- nilpotent group, solvable group