Definition
Group Action
A left action of a group $G$ (Definition~Group (Classical)) on a set $X$ is a map $G \times X \to X$, written $(g, x) \mapsto g \cdot x$, satisfying
\[
e \cdot x = x \quad and \quad g \cdot (h \cdot x) = (gh) \cdot x \quad for all g,h \in G,\, x \in X.
\]
Depends on
Dependency Graph
flowchart LR
classDef current fill:#6366f1,color:#fff,stroke:#4f46e5
n71746aac["Group (Classical)"]
nf7184fc4["Group Action"]:::current
n1641e614["Orbit and Stabilizer"]
n59ff85d3["Direct and Semidirect Product"]
n71746aac --> nf7184fc4
nf7184fc4 --> n1641e614
nf7184fc4 --> n59ff85d3
click n71746aac "../objects/71746aac.html" "_self"
click n1641e614 "../objects/1641e614.html" "_self"
click n59ff85d3 "../objects/59ff85d3.html" "_self"