Central subgroup

From formulasearchengine
Revision as of 10:57, 5 May 2009 by Jitse Niesen (talk | contribs) (add reference)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to navigation Jump to search

In mathematics, in the field of group theory, a subgroup of a group is termed central if it lies inside the center of the group.

Given a group , the center of , denoted as , is defined as the set of those elements of the group which commute with every element of the group. The center is a characteristic subgroup and is also an abelian group (because, in particular, all elements of the center must commute with each other). A subgroup of is termed central if .

Central subgroups have the following properties:


  • {{#invoke:citation/CS1|citation

|CitationClass=citation }}.