Definition:Center (Abstract Algebra)/Group

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

$$Z(G)=\{g \in G|gx=xg, \forall x \in G\}$$.

It is shown here that $$Z(G) \triangleleft G$$ for any group $$G$$.