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