compute the rank of a permutation group
PermGroupRank( G )
a transitive permutation group
The rank of a transitive permutation group G is the number of its sub-orbits, that is, the number of orbits of a point stabiliser. (By convention, the transitivity of an intransitive group is equal to 0.)
The PermGroupRank( G ) command returns the rank of the transitive permutation group G. The group G must be a transitive permutation group. If G is not transitive, an exception is raised.
The alternating and symmetric groups of degree 4 both have rank 2.
To verify this, compute the number of orbits of the stabiliser of a point on the original domain.
Note that the rank is only defined for transitive permutation groups. If the input to the PermGroupRank command is an intransitive group, then an exception is raised, as in the following example.
Error, (in PermGroupRank) permutation group must be transitive
The GroupTheory[PermGroupRank] command was introduced in Maple 2020.
For more information on Maple 2020 changes, see Updates in Maple 2020.
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