center of a group
The center of a group is the subgroup consisting of those elements that commute with every other element. Formally,
It can be shown that the center has the following properties:
It consists of those conjugacy classes containing just one element.
The center of an abelian group is the entire group.
For every prime , every non-trivial finite -group (http://planetmath.org/PGroup4) has a non-trivial center. (Proof of a stronger version of this theorem. (http://planetmath.org/ProofOfANontrivialNormalSubgroupOfAFinitePGroupGAndTheCenterOfGHaveNontrivialIntersection))
A subgroup of the center of a group is called a central subgroup of . All central subgroups of are normal in .
|Title||center of a group|
|Date of creation||2013-03-22 12:23:38|
|Last modified on||2013-03-22 12:23:38|
|Last modified by||yark (2760)|