Stabilizer

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:

G_a = {g ∈ G | a*g = a}

is called the stabilizer of A. G_a is the set of all elements of G which leave a unchanged or 'stable'. G_a is a subgroup of G.

Example

The site-symmetry group of a Wyckoff position is the stabilizer of that position.

See also

• Centralizer
• Normalizer