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group action

A function $G\times X\to X$ , written $g\cdot x$ , satisfying $e\cdot x=x$ and $g\cdot(h\cdot x)=(gh)\cdot x$ for every $g,h\in G$ and $x\in X$ .

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Examples

$D_4$ acting on the four vertices of a square.
$S_n$ acting on $\{1,\ldots,n\}$ by permuting it.