IsDihedral - Maple Help

GroupTheory

 IsDihedral
 determine whether a permutation group is a dihedral group

 Calling Sequence IsDihedral( G )

Parameters

 G - a permutation group

Description

 • The IsDihedral( G ) command determines whether the finite group G is isomorphic to a dihedral group of some (even) order, without using an (expensive) isomorphism test. It returns the value true if G is isomorphic to ${\mathrm{D}}_{n}$, for some positive integer $n$, and returns false otherwise.

Examples

 > $\mathrm{with}\left(\mathrm{GroupTheory}\right):$
 > $G≔\mathrm{Group}\left(\left[\mathrm{Perm}\left(\left[\left[1,2,3,4,5,6,7\right],\left[8,9,10,11,12,13,14\right]\right]\right),\mathrm{Perm}\left(\left[\left[2,7\right],\left[3,6\right],\left[4,5\right],\left[9,14\right],\left[10,13\right],\left[11,12\right]\right]\right)\right]\right)$
 ${G}{≔}⟨\left({1}{,}{2}{,}{3}{,}{4}{,}{5}{,}{6}{,}{7}\right)\left({8}{,}{9}{,}{10}{,}{11}{,}{12}{,}{13}{,}{14}\right){,}\left({2}{,}{7}\right)\left({3}{,}{6}\right)\left({4}{,}{5}\right)\left({9}{,}{14}\right)\left({10}{,}{13}\right)\left({11}{,}{12}\right)⟩$ (1)
 > $\mathrm{GroupOrder}\left(G\right)$
 ${14}$ (2)
 > $\mathrm{IsDihedral}\left(G\right)$
 ${\mathrm{true}}$ (3)
 > $\mathrm{AreIsomorphic}\left(G,\mathrm{DihedralGroup}\left(7\right)\right)$
 ${\mathrm{true}}$ (4)
 > $\mathrm{IsDihedral}\left(\mathrm{QuaternionGroup}\left(\right)\right)$
 ${\mathrm{false}}$ (5)

Compatibility

 • The GroupTheory[IsDihedral] command was introduced in Maple 2019.