A permutation group $G$ (acting on the set$\left\{1\,2\,\dots \,n\right\}$ is regular if it is transitive and the stabilizer of any point is trivial. This means that the action of $G$ is permutation isomorphic  to the action of $G$ on itself by (right) translation.

Every Abelian transitive group is regular.

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

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

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

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

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

$\mathrm{false}$

$\mathrm{IsRegular}\left(\mathrm{CyclicGroup}\left(6\right)\right)$

$\mathrm{true}$

$\mathrm{IsRegular}\left(\mathrm{CyclicGroup}\left(6\,':-\mathrm{mindegree}'\right)\right)$

$\mathrm{false}$

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

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