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Commutator

From Encyclopedia of Mathematics - Reading time: 1 min

of two elements a and b in a group with multiple operators

The element

ab+a+b.

For groups without multiple operators (here the operation is usually called multiplication), the commutator of the elements a and b is the element a1b1ab. The set of all commutators in a group G generates a subgroup, called the commutator subgroup of G.

In an associative algebra the element [x,y]=xyyx is called the Lie product, or commutator, of x and y.


How to Cite This Entry: Commutator (Encyclopedia of Mathematics) | Licensed under CC BY-SA 3.0. Source: https://encyclopediaofmath.org/wiki/Commutator
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