Difference between revisions of "Stabilizer"
From Online Dictionary of Crystallography
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==Example== | ==Example== | ||
| − | The [[site symmetry|site-symmetry group]] of a [[Wyckoff position]] is the stabilizer of that position. | + | The [[site symmetry|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|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|site-symmetry group]]. |
==See also== | ==See also== | ||
Revision as of 11:42, 28 February 2007
Stabilisateur (Fr); Stabilisator (Ge); Stabilizzatore (It); 安定部分群 (Ja).
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.