commutator

commutator (plural commutators)

1. An electrical switch, in a generator or motor, that periodically reverses the direction of an electric current.
2. (group theory) 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. (ring theory) 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.

• anticommutator
• multicommutator

• nilpotent group
• solvable group

• Commutative property on Wikipedia.Wikipedia

commūtātor

1. second-person singular future passive imperative of commūtō
2. third-person singular future passive imperative of commūtō

• commutator in Gaffiot, Félix (1934) Dictionnaire Illustré Latin-Français, Hachette
• commutator in Ramminger, Johann (accessed 16 July 2016) Neulateinische Wortliste: Ein Wörterbuch des Lateinischen von Petrarca bis 1700‎, pre-publication website, 2005-2016