Stabilizer

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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.

See also