GroupTheory - Maple Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Mathematics : Group Theory : GroupTheory package : GroupTheory/ProjectiveGeneralUnitaryGroup

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 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:

n = 2

q <= 100

n = 3

q <= 5

n = 4

q <= 4

n = 5,6

q = 2

• 

The command PGU( n, q ) is provided as an abbreviation.

Examples

withGroupTheory&colon;

ProjectiveGeneralUnitaryGroup2&comma;13

PGU2&comma;13

(1)

GPGU4&comma;4

G:=PGU4&comma;4

(2)

GroupOrderG

1018368000

(3)

IsTransitivePGU3&comma;3

false

(4)

OrbitsPGU3&comma;3

1PGU3&comma;3&comma;2PGU3&comma;3

(5)

GroupOrderPGU4&comma;q

q6q21q3&plus;1q41igcd4&comma;q&plus;1

(6)

Compatibility

• 

The GroupTheory[ProjectiveGeneralUnitaryGroup] command was introduced in Maple 17.

• 

For more information on Maple 17 changes, see Updates in Maple 17.

See Also

GroupTheory[GeneralUnitaryGroup]

GroupTheory[GroupOrder]

GroupTheory[IsTransitive]

GroupTheory[Orbits]

GroupTheory[ProjectiveGeneralLinearGroup]

 


Download Help Document

Was this information helpful?



Please add your Comment (Optional)
E-mail Address (Optional)
What is ? This question helps us to combat spam