##  [Group Action](/group-action) 

  ##  [Group Action](https://algebra.quantumdictionary.io/group-action-0) 

  

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- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A Group Action is a homomorphism from a group G to the permutation group Sym(X) of a set X, equivalently a map G × X → X satisfying e·x = x for the identity e and (gh)·x = g·(h·x) for all g,h ∈ G and x ∈ X; it describes how group elements permute or transform elements of X.