Center (group theory)

The center of a group <math>G</math> (denoted <math>Z(G)</math>) is the set of all elements which 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

• Center on MathWorld