GroupTheory
IsDihedral
determine whether a permutation group is a dihedral group
Calling Sequence
Parameters
Description
Examples
Compatibility
IsDihedral( G )
G
-
a permutation group
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 Dn, for some positive integer n, and returns false otherwise.
withGroupTheory:
G≔GroupPerm1,2,3,4,5,6,7,8,9,10,11,12,13,14,Perm2,7,3,6,4,5,9,14,10,13,11,12
G≔1,2,3,4,5,6,78,9,10,11,12,13,14,2,73,64,59,1410,1311,12
GroupOrderG
14
IsDihedralG
true
AreIsomorphicG,DihedralGroup7
IsDihedralQuaternionGroup
false
Any pair of involutions generates a dihedral group.
G≔McLaughlinGroup:
a≔RandomInvolutionG:
b≔RandomInvolutionG:
IsDihedralGroupa,b
The GroupTheory[IsDihedral] command was introduced in Maple 2019.
For more information on Maple 2019 changes, see Updates in Maple 2019.
See Also
GroupTheory[AreIsomorphic]
GroupTheory[DihedralGroup]
GroupTheory[Group]
GroupTheory[GroupOrder]
GroupTheory[McLaughlinGroup]
GroupTheory[QuaternionGroup]
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