Difference between revisions of "Center (group theory)"
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*We have <math>Z(G) = G</math> if and only if <math>G</math> is an [[abelian group]]. | *We have <math>Z(G) = G</math> if and only if <math>G</math> is an [[abelian group]]. | ||
| − | ==External | + | ==External links== |
*[http://mathworld.wolfram.com/GroupCenter.html Center] on MathWorld | *[http://mathworld.wolfram.com/GroupCenter.html Center] on MathWorld | ||
[[Category:Algebra]] | [[Category:Algebra]] | ||
Latest revision as of 05:47, July 13, 2016
The center of a group (denoted ) is the set of all elements which commute with every element of the group. That is, the center of is .
Facts
- If is a group, the center is a normal subgroup of .
- We have if and only if is an abelian group.
External links
- Center on MathWorld