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Center

From Online Dictionary of Crystallography

Revision as of 13:59, 27 August 2014 by MassimoNespolo (talk | contribs) (see also)

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


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: gaga-1.

See also