Group action

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Definition

A group action of a group $G$ on a set $A$ is a map from $G\times A \to A$ usually written as $g\cdot a$ for all $g\in G$ and $a\in A$, that satisfies the following two properties:

• $g_1 \cdot(g_2\cdot a) =(g_1g_2)\cdot a$ for all $g_1,g_2\in G,a\in A$