attempt to determine whether a group is Hamiltonian
attempt to determine whether a group is Dedekind
IsDedekind( G )
IsHamiltonian( G )
a permutation group
A group G is Dedekind if every subgroup of G is normal in G. Every Abelian group is obviously a Dedekind group, but non-Abelian Dedekind groups exist.
A group G is Hamiltonian if it is a non-commutative Dedekind group.
The IsDedekind( G ) command attempts to determine whether the group G is Dedekind. It returns true if G is Dedekind and returns false otherwise.
The IsHamiltonian( G ) command attempts to determine whether the group G is Hamiltonian, returning true if G is Hamiltonian, and false otherwise.
The smallest Hamiltonian group is the quaternion group of order 8.
The fact that this group is Hamiltonian is visible from the subgroup lattice:
You can see that the dihedral group of order 8 is not Hamiltonian by looking at its subgroup lattice.
The GroupTheory[IsHamiltonian] and GroupTheory[IsDedekind] commands were introduced in Maple 2019.
For more information on Maple 2019 changes, see Updates in Maple 2019.
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