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The '''center''' of a [[Group (mathematics)|group]] <math>G</math> (denoted <math>Z(G)</math>) is the set of all elements which [[Commutativity|commute]] with every element of the group. That is, the center of <math>G</math> is <math>\{a \in G : ab=ba\ \forall b \in G\}</math>.
The '''center''' of a [[Group (mathematics)|group]] <math>G</math> (denoted <math>Z(G)</math>) is the set of all elements which [[Commutativity|commute]] with every element of the group. That is, the center of <math>G</math> is <math>\{a \in G : ab=ba\ \forall b \in G\}</math>.
==Facts==
*If <math>G</math> is a group, the center <math>Z(G)</math> is a [[normal subgroup]] of <math>G</math>.
*We have <math>Z(G) = G</math> if and only if <math>G</math> is an [[abelian group]].
==External Links==
==External Links==
*[http://mathworld.wolfram.com/GroupCenter.html Center] on MathWorld
*[http://mathworld.wolfram.com/GroupCenter.html Center] on MathWorld
[[Category:Algebra]]
[[Category:Algebra]]