Difference between revisions of "Center"
From Online Dictionary of Crystallography
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| − | <font color="blue">Centre</font> (''Fr''). <font color="red">Zentrum</font> (''Ge''). <font color=" | + | <font color="orange">مركز</font> (''Ar''). <font color="blue">Centre</font> (''Fr''). <font color="red">Zentrum</font> (''Ge''). <font color="black">Centro</font> (''It''). <font color="purple">中心</font> (''Ja''). <font color="green">Centro</font> (''Sp''). |
Latest revision as of 17:00, 9 November 2017
مركز (Ar). Centre (Fr). Zentrum (Ge). Centro (It). 中心 (Ja). Centro (Sp).
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.