Past exam of the mathematics course of the University of Oxford / 2014 / Prelims / Mathematics I / 7 / a / i

A left group action of $G$ on a set $S$ is a function $\varphi :G\times S\to S$ satisfyingfor all $s\in S$ and $g,h\in G$. Writing $g\cdot s=\varphi (g,s)$, these are $e\cdot s=s$ and $(gh)\cdot s=g\cdot (h\cdot s)$. No commutativity is assumed, so the order of composition matters.