For any group , , the center of . Thus, any subgroup of is an abelian subgroup of . However, the converse is generally not true. For example, take any non-abelian group and pick any element not in the center. Then the subgroup generated by it is obviously abelian, clearly non-trivial and not contained in the center.
|Date of creation||2013-03-22 14:01:20|
|Last modified on||2013-03-22 14:01:20|
|Last modified by||yark (2760)|