attempt to determine whether a group has perfect order classes
IsPerfectOrderClassesGroup( G )
a finite group
A finite group G is said to have perfect order classes (or subsets) if the length of each of its order classes is a divisor of the order of G.
Apart from the trivial group, every group with perfect order classes has even order.
The IsPerfectOrderClassesGroup( G ) command attempts to determine whether the group G is a group with perfect order classes. It returns true if G has perfect order classes, and returns false otherwise.
These next two examples demonstrate that the groups with perfect order classes are closed under neither subgroups or quotients.
The GroupTheory[IsPerfectOrderClassesGroup] command was introduced in Maple 2019.
For more information on Maple 2019 changes, see Updates in Maple 2019.
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