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GroupTheory

  

ProjectiveGeneralUnitaryGroup

  

construct a permutation group isomorphic to a projective general unitary group

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

ProjectiveGeneralUnitaryGroup(n, q)

PGU(n, q)

Parameters

n

-

a positive integer greater than 1

q

-

power of a prime number

Description

• 

The projective general unitary group PGUn,q is the quotient of the general unitary group GUn,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 PGUn,q and PGLn,q are isomorphic, so the latter is returned in this case.

• 

The ranges for n and q which are implemented are as follows:

n=2

q100

n=3

q5

n=4

q4

n=5,6

q=2

• 

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.

Examples

withGroupTheory:

ProjectiveGeneralUnitaryGroup2,13

PGU2,13

(1)

GPGU4,4

GPGU4,4

(2)

GroupOrderG

1018368000

(3)

IsTransitivePGU3,3

true

(4)

IsPrimitivePGU3,3

true

(5)

GroupOrderPGU4,q

q6q21q3+1q41

(6)

Compatibility

• 

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.

See Also

GroupTheory[GeneralUnitaryGroup]

GroupTheory[GroupOrder]

GroupTheory[IsTransitive]

GroupTheory[Orbits]

GroupTheory[ProjectiveGeneralLinearGroup]