Difference between revisions of "Center"
From Online Dictionary of Crystallography
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| − | <font color="blue">Centre</font> (''Fr'') | + | <font color="blue">Centre</font> (''Fr''); <font color="red">Zentrum</font> (''Ge''); <font color="green">Centro</font> (''Sp''); <font color="black">Centro</font> (''It''); <font color="purple">中心</font> (''Ja''); <font color="orange">مركز</font> (''Ar''). |
Revision as of 09:14, 14 September 2017
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: g → aga-1.