stabilizer of a group action

群作用的稳定化子

Algebra & Algebraic Geometry · Undergraduate · Mathematics Resources editorial compilation (AI-assisted)

Translation evidence: Literature usage

Meaning in context

The subgroup Gx={g∈G:gx=x}G_x=\{g\in G:gx=x\} fixing a specified point.

使指定点保持不动的所有群元素组成的子群。

Example

A square vertex has stabilizer of order two in its eight-element symmetry group.

Usage and distinctions

The stabilizer fixes one point; the action kernel fixes every point.

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Definition sources

  1. Wen-Wei Li — Methods in Algebra I, author source群作用和计数原理 (sec:group-action), same definition's G_x={g:gx=x} clause naming 稳定化子, followed by its group specialization · Checked 2026-10-15

Translation sources

  1. 李文威 — 代数学方法 卷一，作者源文件群作用和计数原理 (sec:group-action), same definition's G_x={g:gx=x} clause naming 稳定化子, followed by its group specialization · Checked 2026-10-15
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