construct a permutation group isomorphic to a projective general unitary group
a positive integer greater than 1
power of a prime number
The projective general unitary group PGU⁡n,q is the quotient of the general unitary group GU⁡n,q by its center.
The ProjectiveGeneralUnitaryGroup( n, q ) command returns a permutation group isomorphic to the projective general unitary group of degree n over the field with q2 elements. In general, this is not a transitive representation.
Note that for n=2 the groups PGU⁡n,q and PGL⁡n,q are isomorphic, so the latter is returned in this case.
The ranges for n and q which are implemented are as follows:
If either or both of the arguments n and q are non-numeric, then a symbolic group representing the projective general unitary group is returned.
The command PGU( 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.
ProjectiveGeneralUnitaryGroup( 2, 13 );
G := PGU( 4, 4 );
GroupOrder( G );
IsTransitive( PGU( 3, 3 ) );
IsPrimitive( PGU( 3, 3 ) );
GroupOrder( PGU( 4, q ) );
The GroupTheory[ProjectiveGeneralUnitaryGroup] command was introduced in Maple 17.
For more information on Maple 17 changes, see Updates in Maple 17.
The GroupTheory[ProjectiveGeneralUnitaryGroup] command was updated in Maple 2020.
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