Group action
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Definition
A group action of a group [ilmath]G[/ilmath] on a set [ilmath]A[/ilmath] is a map from [ilmath]G\times A \to A[/ilmath] usually written as [ilmath]g\cdot a[/ilmath] for all [ilmath]g\in G[/ilmath] and [ilmath]a\in A[/ilmath], that satisfies the following two properties:
- [ilmath]g_1 \cdot(g_2\cdot a) =(g_1g_2)\cdot a[/ilmath] for all [ilmath]g_1,g_2\in G,a\in A[/ilmath]
