Center

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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 fa: gaga-1.

See also