Difference between revisions of "Center"
From Online Dictionary of Crystallography
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of the [[group homomorphism|homomorphism]] mapping an element ''a'' of ''G'' to the [[automorphism|inner automorphism]] ''f<sub>a</sub>'': ''g'' → ''aga<sup>-1</sup>''. | of the [[group homomorphism|homomorphism]] mapping an element ''a'' of ''G'' to the [[automorphism|inner automorphism]] ''f<sub>a</sub>'': ''g'' → ''aga<sup>-1</sup>''. | ||
| − | + | ==See also== | |
| + | *[[Centralizer]] | ||
| + | *[[Normalizer]] | ||
| + | *[[Stabilizer]] | ||
[[Category:Fundamental crystallography]] | [[Category:Fundamental crystallography]] | ||
Revision as of 13:59, 27 August 2014
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: g → aga-1.