The centralizer of an element 
of a group 
is the set of elements of 
which commute with 
,
 |
Likewise, the centralizer of a subgroup 
of a group 
is the set of elements of 
which commute with every element of 
,
 |
The centralizer always contains the group center of the group and is contained in the corresponding normalizer. In an Abelian group, the centralizer is the whole group.
