Group action (awaiting review)

A (left) group action of a group $G$ on a set $A$ is a function $ \cdot : G\times A \to A $ such that

• for all $a\in A$, $e\cdot a = a$ where $e$ is the identity element of $G$
• for all $g,h\in G$ and all $a\in A$, $g\cdot (h\cdot a) = (gh)\cdot a$.

The action is transitive if for all $a,b\in A$, there exists $g\in G$ such that $g\cdot a = b$.