Difference between revisions of "Center"
From Online Dictionary of Crystallography
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Revision as of 11:34, 2 April 2009
Centre (Fr); Zentrum (Ge); Centro (Sp); Centro (It).
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 fa: g → aga-1.