Center

Centre (Fr); Zentrum (Ge); Centro (Sp); Centro (It); 中心 (Ja); مركز (Ar).

The centre (or center) 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 centre is an Abelian group.

The centre 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.

See also

• Centralizer
• Normalizer
• Stabilizer