group action

群作用

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

Translation evidence: Literature usage

Meaning in context

A map G×X→XG\times X\to X with ex=xex=x and (gh)x=g(hx)(gh)x=g(hx); this is a left action.

满足单位元作用恒等且与群乘法相容的映射 G×X→XG\times X\to X；此处取左作用。

Example

S3S_3 acts on {1,2,3}\{1,2,3\} by permutations.

Usage and distinctions

A right action has a different order convention; an arbitrary assignment of permutations is insufficient.

Read the encyclopedia explanation

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 def:monoid-action (幺半群的作用), left action clauses (i)–(ii); specialize the monoid to a group · 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 def:monoid-action (幺半群的作用), left action clauses (i)–(ii); specialize the monoid to a group · Checked 2026-10-15
Edit source / propose a PRReport a correction

Original encyclopedia and terminology content: CC BY-SA 4.0. Contribute or report a correction.