The centralizer subgroup (also: commutant) of a subset in (the set underlying) a group is the subgroup
of all elements which commute with , hence such that for all .
Notice the similarity with but difference to the concept of normalizer subgroup.
The centralizer of is clearly a subgroup of its normalizer
as fixing the set is a weaker requirement than for all .
See also
Last revised on November 6, 2020 at 15:00:13. See the history of this page for a list of all contributions to it.