# Commutator

From Encyclopedia of Mathematics

*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 .

**How to Cite This Entry:**

Commutator.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Commutator&oldid=16944

This article was adapted from an original article by O.A. Ivanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article