Category:Centers of Groups

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This category contains results about Centers of Groups.


The center of a group $G$, denoted $\map Z G$, is the subset of elements in $G$ that commute with every element in $G$.

Symbolically:

$\map Z G = \map {C_G} G = \set {g \in G: g x = x g, \forall x \in G}$


That is, the center of $G$ is the centralizer of $G$ in $G$ itself.