A permutation group $G$ (acting on the set$\left\{1\,2\,\dots \,n\right\}$ is transitive if, for any $\mathrm{\alpha }$ and $\mathrm{\beta }$, there is a permutation $g$ in $G$ for which ${\mathrm{\alpha }}^g=\mathrm{\beta }$. Alternatively, $G$ is transitive if it has precisely one orbit.

The IsTransitive( G ) command returns true if the permutation group G is transitive, and returns false otherwise. The group G must be an instance of a permutation group.

$\mathrm{with}\left(\mathrm{GroupTheory}\right)\:$

$G≔\mathrm{PermutationGroup}\left(\left\{\left[\left[1\,2\right]\right]\,\left[\left[1\,2\,3\right]\,\left[4\,5\right]\right]\right\}\right)$

$G≔⟨\left(1\,2\right)\,\left(1\,2\,3\right)\left(4\,5\right)⟩$

$\mathrm{IsTransitive}\left(G\right)$

$\mathrm{false}$

$\mathrm{IsTransitive}\left(\mathrm{AlternatingGroup}\left(4\right)\right)$

$\mathrm{true}$

The GroupTheory[IsTransitive] command was introduced in Maple 17.

For more information on Maple 17 changes, see Updates in Maple 17.