construct a permutation group isomorphic to a projective special unitary group
ProjectiveSpecialUnitaryGroup( n, q )
PSU( n, q )
a positive integer
power of a prime number
The projective special unitary group PSU⁡n,q , over the field with q2 elements, is the quotient of the special unitary group SU⁡n,q by its center.
Note that for n=2 the groups PSU⁡n,q andPSL⁡n,q are isomorphic. These groups are soluble being isomorphic, respectively, to the symmetric group of order 6, and the alternating group of order 12. Furthermore, the group PSU⁡3,2 is a Frobenius group of order 72 and is soluble. For all other values of n and q, the groupPSU⁡n,q is simple.
The ProjectiveSpecialUnitaryGroup( n, q ) command returns a permutation group isomorphic to the projective special unitary group PSU⁡n,q for values of the parameters n and q in the implemented ranges.
The implemented ranges for n and q are as follows:
If either or both of the arguments n and q are non-numeric, then a symbolic group representing the projective special unitary group is returned.
The command PSU( n, q ) is provided as an abbreviation.
In the Standard Worksheet interface, you can insert this group into a document or worksheet by using the Group Constructors palette.
The GroupTheory[ProjectiveSpecialUnitaryGroup] command was introduced in Maple 17.
For more information on Maple 17 changes, see Updates in Maple 17.
The GroupTheory[ProjectiveSpecialUnitaryGroup] command was updated in Maple 2020.
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