IsRegular - Maple Help

GroupTheory

 IsRegular
 determine whether a permutation group is regular

 Calling Sequence IsRegular( G )

Parameters

 G - a permutation group

Description

 • 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.

Examples

 > $\mathrm{with}\left(\mathrm{GroupTheory}\right):$
 > $G≔\mathrm{Group}\left(\left\{\mathrm{Perm}\left(\left[\left[1,2\right]\right]\right),\mathrm{Perm}\left(\left[\left[1,2,3\right],\left[4,5\right]\right]\right)\right\}\right)$
 ${G}{≔}⟨\left({1}{,}{2}\right){,}\left({1}{,}{2}{,}{3}\right)\left({4}{,}{5}\right)⟩$ (1)
 > $\mathrm{IsRegular}\left(G\right)$
 ${\mathrm{false}}$ (2)
 > $\mathrm{IsRegular}\left(\mathrm{CyclicGroup}\left(6\right)\right)$
 ${\mathrm{true}}$ (3)
 > $\mathrm{IsRegular}\left(\mathrm{CyclicGroup}\left(6,':-\mathrm{mindegree}'\right)\right)$
 ${\mathrm{false}}$ (4)

Compatibility

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