Center (group theory)

In abstract algebra, the center of a group G, denoted Z(G), is the set of elements that commute with every element of G. In set-builder notation,

The center is a subgroup of G, which by definition is abelian (that is, commutative). As a subgroup, it is always normal, and indeed characteristic, but it need not be fully characteristic. The quotient group G / Z(G) is isomorphic to the group of inner automorphisms of G.