# Stabilizer

(Difference between revisions)
 Revision as of 12:42, 13 October 2017 (view source) (languages)← Older edit Revision as of 08:49, 20 November 2017 (view source)m (Tidied translations.)Newer edit → Line 1: Line 1: - Stabilisateur (''Fr''); Stabilisator (''Ge''); Stabilizzatore (''It''); 安定部分群 (''Ja''); Стабилизатор (''Ru''); Estabilizador (''Sp''). + Stabilisateur (''Fr''). Stabilisator (''Ge''). Stabilizzatore (''It''). 安定部分群 (''Ja''). Стабилизатор (''Ru''). Estabilizador (''Sp''). + + + Synonym: isotropy group.

## Revision as of 08:49, 20 November 2017

Stabilisateur (Fr). Stabilisator (Ge). Stabilizzatore (It). 安定部分群 (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 = {gG | 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.