orbit of a group action

群作用的轨道

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

Translation evidence: Literature usage

Meaning in context

For $x$ in a $G$-set, the subset $Gx=\{gx:g\in G\}$.

给定群作用下，一个点经所有群元素变换所能到达的点的集合。

Example

The square symmetry group has one orbit on vertices.

Usage and distinctions

A group orbit is unrelated to iteration of a single map unless the action is specified.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

1. Wen-Wei Li — Methods in Algebra I, author source群作用和计数原理 (sec:group-action), definition of Gx={gx:g∈G} naming 轨道, 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), definition of Gx={gx:g∈G} naming 轨道, followed by its group specialization · Checked 2026-10-15

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