1.18: Center
The center (or centre ) of a group G is the set Z(G) = { a in G : a*g = g*a for all g in G } of elements commuting with all elements of G . The center is an Abelian group.
The center of a group G is always a normal subgroup of G , namely the kernel of the homomorphism mapping an element a of G to the inner automorphism f a : g → aga -1 .