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. O.A. Ivanova (originator), Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Commutator&oldid=16944
Commutator. O.A. Ivanova (originator), Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Commutator&oldid=16944
This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098