A <group action> assigns to each $g\in G$ and $x\in\Omega$ a point $g\cdot x$ so that $1\cdot x=x$ and $(gh)\cdot x=g\cdot(h\cdot x)$. The <orbit> of $x$ is $Gx=\{g\cdot x:g\in G\}$. The action is <transitive> if there is exactly one <orbit>, equivalently any point can be carried to any other by some group element.

Solution

Past exam of the options II course of the University of Oxford / 2009 / B / B2 / i / Solution

 Solution (source code)