From Encyclopedia of Mathematics - Reading time: 1 min
of two elements and in a group with multiple operators
The element
For groups without multiple operators (here the operation is usually called multiplication), the commutator of the elements and is the element . The set of all commutators in a group generates a subgroup, called the commutator subgroup of .
In an associative algebra the element is called the Lie product, or commutator, of and .