Difference between revisions of "Stabilizer"
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| − | <font color="blue">Stabilisateur</font> (''Fr''). <font color="red">Stabilisator</font> (''Ge''). <font color="black">Stabilizzatore</font> (''It''). <font color="purple"> | + | <font color="blue">Stabilisateur</font> (''Fr''). <font color="red">Stabilisator</font> (''Ge''). <font color="black">Stabilizzatore</font> (''It''). <font color="purple">安定群</font> (''Ja''). <font color="brown">Стабилизатор</font> (''Ru''). <font color="green">Estabilizador</font> (''Sp''). |
Latest revision as of 16:06, 28 November 2018
Stabilisateur (Fr). Stabilisator (Ge). Stabilizzatore (It). 安定群 (Ja). Стабилизатор (Ru). Estabilizador (Sp).
Synonym: isotropy group.
Let G be a group which acts on a set A by a composition law *, and let a be a given element of A. Then the set
Ga = {g ∈ G | a*g = a}
is called the stabilizer of A. Ga is the set of all elements of G which leave a unchanged or 'stable'. Ga is a subgroup of G.
Example
The site-symmetry group of a Wyckoff position is the stabilizer of that position. In this example, G is the space group, the stabilizer is the site-symmetry group, the set A is the set of triples of x,y,z coordinates (set of points in the three-dimensional space), the element a that is 'stable' under the action of the stabilizer is the Wyckoff position which corresponds to that site-symmetry group.